diff --git a/collects/scribblings/gui/clipboard-intf.scrbl b/collects/scribblings/gui/clipboard-intf.scrbl
index 230949287a..008ffca46e 100644
--- a/collects/scribblings/gui/clipboard-intf.scrbl
+++ b/collects/scribblings/gui/clipboard-intf.scrbl
@@ -28,7 +28,7 @@ Generic data is always retrieved from the clipboard as a byte
  clipboard formats is determined by the current clipboard owner.
 
 
-@defmethod[(get-clipboard-bitmap [time (and/c exact? integer?)])
+@defmethod[(get-clipboard-bitmap [time exact-integer?])
            (or/c (is-a?/c bitmap%) false/c)]{
 
 Gets the current clipboard contents as a bitmap (Windows, Mac OS X),
@@ -44,7 +44,7 @@ See @|timediscuss| for a discussion of the @scheme[time] argument.  If
 }
 
 @defmethod[(get-clipboard-data [format string]
-                               [time (and/c exact? integer?)])
+                               [time exact-integer?])
            (or/c bytes? string? false/c)]{
 
 Gets the current clipboard contents in a specific format, returning
@@ -65,7 +65,7 @@ See @|timediscuss| for a discussion of the @scheme[time] argument.  If
 
 }
 
-@defmethod[(get-clipboard-string [time (and/c exact? integer?)])
+@defmethod[(get-clipboard-string [time exact-integer?])
            (or/c string false/c)]{
 
 Gets the current clipboard contents as simple text, returning
@@ -89,7 +89,7 @@ Returns @scheme[#t] if @scheme[owner] currently owns the clipboard,
 
 
 @defmethod[(set-clipboard-bitmap [new-bitmap (is-a?/c bitmap%)]
-                                 [time (and/c exact? integer?)])
+                                 [time exact-integer?])
            void?]{
 
 Changes the current clipboard contents to @scheme[new-bitmap] (Windows, Mac OS X)
@@ -102,7 +102,7 @@ See @|timediscuss| for
 }
 
 @defmethod[(set-clipboard-client [new-owner (is-a?/c clipboard-client%)]
-                                 [time (and/c exact? integer?)])
+                                 [time exact-integer?])
            void?]{
 
 Changes the clipboard-owning client: sets the client to
@@ -118,7 +118,7 @@ See @|timediscuss| for a discussion of the @scheme[time] argument. If
 }
 
 @defmethod[(set-clipboard-string [new-text string]
-                                 [time (and/c exact? integer?)])
+                                 [time exact-integer?])
            void?]{
 
 Changes the current clipboard contents to @scheme[new-text],
diff --git a/collects/scribblings/gui/control-event-class.scrbl b/collects/scribblings/gui/control-event-class.scrbl
index 1912333746..6e60a54532 100644
--- a/collects/scribblings/gui/control-event-class.scrbl
+++ b/collects/scribblings/gui/control-event-class.scrbl
@@ -11,7 +11,7 @@ A @scheme[control-event%] object contains information about a
                                        'list-box 'list-box-dclick 'text-field 
                                        'text-field-enter 'slider 'radio-box 
                                        'menu-popdown 'menu-popdown-none 'tab-panel)]
-                [time-stamp (and/c exact? integer?) 0])]{
+                [time-stamp exact-integer? 0])]{
 
 The @scheme[event-type] argument is one of the following:
 @itemize[
diff --git a/collects/scribblings/gui/editor-intf.scrbl b/collects/scribblings/gui/editor-intf.scrbl
index ada8f3efa6..7c851d5fdd 100644
--- a/collects/scribblings/gui/editor-intf.scrbl
+++ b/collects/scribblings/gui/editor-intf.scrbl
@@ -230,7 +230,7 @@ Starts a sequence.
 
 @defmethod[(begin-write-header-footer-to-file [f (is-a?/c editor-stream-out%)]
                                               [name string?]
-                                              [buffer (box/c (and/c exact? integer?))])
+                                              [buffer (box/c exact-integer?)])
            void?]{
 
 This method must be called before writing any special header data to a
@@ -369,7 +369,7 @@ Destroys the undo history of the editor.
 }
 
 @defmethod[(copy [extend? any/c #f]
-                 [time (and/c exact? integer?) 0])
+                 [time exact-integer? 0])
            void?]{
 
 Copies @techlink{item}s into the clipboard. If @scheme[extend?] is not
@@ -413,7 +413,7 @@ style list is copied and the copy is installed as the style list for
 }
 
 @defmethod[(cut [extend? any/c #f]
-                [time (and/c exact? integer?) 0])
+                [time exact-integer? 0])
            void?]{
 
 Copies and then deletes the currently selected @techlink{item}s. If
@@ -466,7 +466,7 @@ See @xmethod[text% do-copy] or @xmethod[pasteboard% do-copy].}
                                         'kill 'select-all 'insert-text-box 
                                         'insert-pasteboard-box 'insert-image)]
                               [recursive? any/c #t]
-                              [time (and/c exact? integer?) 0])
+                              [time exact-integer? 0])
            void?]{
 
 Performs a generic edit command. The @scheme[op] argument must be a
@@ -532,7 +532,7 @@ See @method[editor<%> begin-edit-sequence].
 }
 
 @defmethod[(end-write-header-footer-to-file [f (is-a?/c editor-stream-out%)]
-                                            [buffer-value (and/c exact? integer?)])
+                                            [buffer-value exact-integer?])
            void?]{
 
 This method must be called after writing any special header data to a
@@ -1061,7 +1061,7 @@ Returns @scheme[#t] if the editor is currently being printed through
 the @method[editor<%> print] method, @scheme[#f] otherwise.}
 
 
-@defmethod[(kill [time (and/c exact? integer?) 0])
+@defmethod[(kill [time exact-integer? 0])
            void?]{
 
 In a text editor, cuts to the end of the current line, or cuts a
@@ -1674,7 +1674,7 @@ Propagates the flag to any snip with the editor-local focus. If no
 }}
 
 
-@defmethod[(paste [time (and/c exact? integer?) 0])
+@defmethod[(paste [time exact-integer? 0])
            void?]{
 
 Pastes the current contents of the clipboard into the editor.
@@ -1693,7 +1693,7 @@ See also @method[editor<%> get-paste-text-only].
 }
 
 
-@defmethod[(paste-x-selection [time (and/c exact? integer?) 0])
+@defmethod[(paste-x-selection [time exact-integer? 0])
            void?]{
 
 Like @method[editor<%> paste], but under X, uses the X selection
diff --git a/collects/scribblings/gui/editor-stream-in-class.scrbl b/collects/scribblings/gui/editor-stream-in-class.scrbl
index 4cf7153b9c..9b2f2578f5 100644
--- a/collects/scribblings/gui/editor-stream-in-class.scrbl
+++ b/collects/scribblings/gui/editor-stream-in-class.scrbl
@@ -17,7 +17,7 @@ An in-stream base---possibly an @scheme[editor-stream-in-bytes-base%]
 }
 
 
-@defmethod*[([(get [v (box/c (and/c exact? integer?))])
+@defmethod*[([(get [v (box/c exact-integer?)])
               (is-a?/c editor-stream-in%)]
              [(get [v (box/c real?)])
               (is-a?/c editor-stream-in%)])]{
@@ -45,13 +45,13 @@ Like @method[editor-stream-in% get-unterminated-bytes], but the last
 }
 
 @defmethod[(get-exact)
-           (and/c exact? integer?)]{
+           exact-integer?]{
 
 Returns the next integer value in the stream.
 
 }
 
-@defmethod[(get-fixed [v (box/c (and/c exact? integer?))])
+@defmethod[(get-fixed [v (box/c exact-integer?)])
            (is-a?/c editor-stream-in%)]{
 
 @boxisfill[(scheme v) @elem{a fixed-size integer from the stream obtained through 
@@ -60,7 +60,7 @@ Returns the next integer value in the stream.
 }
 
 @defmethod[(get-fixed-exact)
-           (and/c exact? integer?)]{
+           exact-integer?]{
 
 Gets a fixed-sized integer from the stream. See
 @method[editor-stream-out% put-fixed] for more information.
diff --git a/collects/scribblings/gui/editor-stream-out-class.scrbl b/collects/scribblings/gui/editor-stream-out-class.scrbl
index 16001d5049..8a7ff58520 100644
--- a/collects/scribblings/gui/editor-stream-out-class.scrbl
+++ b/collects/scribblings/gui/editor-stream-out-class.scrbl
@@ -54,7 +54,7 @@ This method is called by @scheme[write-editor-global-header].
               (is-a?/c editor-stream-out%)]
              [(put [v bytes?])
               (is-a?/c editor-stream-out%)]
-             [(put [v (and/c exact? integer?)])
+             [(put [v exact-integer?])
               (is-a?/c editor-stream-out%)]
              [(put [v real?])
               (is-a?/c editor-stream-out%)])]{
@@ -77,7 +77,7 @@ If @scheme[n] is not supplied and @scheme[v] is a byte string, then
 }
 
 
-@defmethod[(put-fixed [v (and/c exact? integer?)])
+@defmethod[(put-fixed [v exact-integer?])
            (is-a?/c editor-stream-out%)]{
 
 Puts a fixed-sized integer into the stream. This method is needed
diff --git a/collects/scribblings/gui/event-class.scrbl b/collects/scribblings/gui/event-class.scrbl
index 007eb27cb9..dcb64ecedf 100644
--- a/collects/scribblings/gui/event-class.scrbl
+++ b/collects/scribblings/gui/event-class.scrbl
@@ -11,7 +11,7 @@ keyboard, mouse, or scroll event. See also
 @scheme[scroll-event%].
 
 
-@defconstructor[([time-stamp (and/c exact? integer?) 0])]{
+@defconstructor[([time-stamp exact-integer? 0])]{
 
 See @method[event% get-time-stamp] for information about
  @scheme[time-stamp].
@@ -19,7 +19,7 @@ See @method[event% get-time-stamp] for information about
 }
 
 @defmethod[(get-time-stamp)
-           (and/c exact? integer?)]{
+           exact-integer?]{
 
 Returns the time, in milliseconds, when the event occurred. This time
  is compatible with times reported by MzScheme's
@@ -27,7 +27,7 @@ Returns the time, in milliseconds, when the event occurred. This time
 
 }
 
-@defmethod[(set-time-stamp [time (and/c exact? integer?)])
+@defmethod[(set-time-stamp [time exact-integer?])
            void?]{
 
 Set the time, in milliseconds, when the event occurred. See also
diff --git a/collects/scribblings/gui/font-class.scrbl b/collects/scribblings/gui/font-class.scrbl
index 87eea93bec..ee29304307 100644
--- a/collects/scribblings/gui/font-class.scrbl
+++ b/collects/scribblings/gui/font-class.scrbl
@@ -141,7 +141,7 @@ families.
 }
 
 @defmethod[(get-font-id)
-           (and/c exact? integer?)]{
+           exact-integer?]{
 
 Gets the font's ID, for use with a
 @scheme[font-name-directory<%>]. The ID is determined by the font's
diff --git a/collects/scribblings/gui/font-name-directory-intf.scrbl b/collects/scribblings/gui/font-name-directory-intf.scrbl
index 3d50f9ec49..49b6ee799e 100644
--- a/collects/scribblings/gui/font-name-directory-intf.scrbl
+++ b/collects/scribblings/gui/font-name-directory-intf.scrbl
@@ -99,7 +99,7 @@ The mapping for face names can be overridden (on all platforms)
 
 @defmethod[(find-family-default-font-id [family (one-of/c 'default 'decorative 'roman 'script 
                                                           'swiss 'modern 'symbol 'system)])
-           (and/c exact? integer?)]{
+           exact-integer?]{
 
 Gets the font ID representing the default font for a family. See
 @scheme[font%] for information about font families.
@@ -109,7 +109,7 @@ Gets the font ID representing the default font for a family. See
 @defmethod[(find-or-create-font-id [name string?]
                                    [family (one-of/c 'default 'decorative 'roman 'script 
                                                      'swiss 'modern 'symbol 'system)])
-           (and/c exact? integer?)]{
+           exact-integer?]{
 
 Gets the face name for a font ID, initializing the mapping for
  the face name if necessary.
@@ -119,7 +119,7 @@ Font ID are useful only as mapping indices for
 
 }
 
-@defmethod[(get-face-name [font-id (and/c exact? integer?)])
+@defmethod[(get-face-name [font-id exact-integer?])
            (or/c string? false/c)]{
 
 Gets the face name for a font ID. If the font ID corresponds to
@@ -127,7 +127,7 @@ Gets the face name for a font ID. If the font ID corresponds to
 
 }
 
-@defmethod[(get-family [font-id (and/c exact? integer?)])
+@defmethod[(get-family [font-id exact-integer?])
            (one-of/c 'default 'decorative 'roman 'script 
                      'swiss 'modern 'symbol 'system)]{
 
@@ -139,7 +139,7 @@ Gets the family for a font ID. See
 @defmethod[(get-font-id [name string?]
                         [family (one-of/c 'default 'decorative 'roman 'script 
                                           'swiss 'modern 'symbol 'system)])
-           (and/c exact? integer?)]{
+           exact-integer?]{
 
 Gets the font ID for a face name paired with a default family. If the
  mapping for the given pair is not already initialized, @scheme[0] is
@@ -151,7 +151,7 @@ Font ID are useful only as mapping indices for
 
 }
 
-@defmethod[(get-post-script-name [font-id (and/c exact? integer?)]
+@defmethod[(get-post-script-name [font-id exact-integer?]
                                  [weight (one-of/c 'normal 'bold 'light)]
                                  [style (one-of/c 'normal 'italic 'slant)])
            (or/c string? false/c)]{
@@ -166,7 +166,7 @@ See @scheme[font%] for information about @scheme[weight] and
 
 }
 
-@defmethod[(get-screen-name [font-id (and/c exact? integer?)]
+@defmethod[(get-screen-name [font-id exact-integer?]
                             [weight (one-of/c 'normal 'bold 'light)]
                             [style (one-of/c 'normal 'italic 'slant)])
            (or/c string? false/c)]{
@@ -180,7 +180,7 @@ See @scheme[font%] for information about @scheme[weight] and
 
 }
 
-@defmethod[(set-post-script-name [font-id (and/c exact? integer?)]
+@defmethod[(set-post-script-name [font-id exact-integer?]
                                  [weight (one-of/c 'normal 'bold 'light)]
                                  [style (one-of/c 'normal 'italic 'slant)]
                                  [name string?])
@@ -194,7 +194,7 @@ See @scheme[font%] for information about @scheme[weight] and @scheme[style].
 
 }
 
-@defmethod[(set-screen-name [font-id (and/c exact? integer?)]
+@defmethod[(set-screen-name [font-id exact-integer?]
                             [weight (one-of/c 'normal 'bold 'light)]
                             [style (one-of/c 'normal 'italic 'slant)]
                             [name string?])
diff --git a/collects/scribblings/gui/key-event-class.scrbl b/collects/scribblings/gui/key-event-class.scrbl
index 197798ec51..d4be50baed 100644
--- a/collects/scribblings/gui/key-event-class.scrbl
+++ b/collects/scribblings/gui/key-event-class.scrbl
@@ -21,9 +21,9 @@ See also @|mousekeydiscuss|.
                  [control-down any/c #f]
                  [meta-down any/c #f]
                  [alt-down any/c #f]
-                 [x (and/c exact? integer?) 0]
-                 [y (and/c exact? integer?) 0]
-                 [time-stamp (and/c exact? integer?) 0]
+                 [x exact-integer? 0]
+                 [y exact-integer? 0]
+                 [time-stamp exact-integer? 0]
                  [caps-down any/c #f])]{
 
 See the corresponding @schemeidfont{get-} and @schemeidfont{set-}
@@ -264,7 +264,7 @@ Returns @scheme[#t] if the Shift key was down for the event.
 }
 
 @defmethod[(get-x)
-           (and/c exact? integer?)]{
+           exact-integer?]{
 
 Returns the x-position of the mouse at the time of the event, in the
  target's window's (client-area) coordinate system.
@@ -272,7 +272,7 @@ Returns the x-position of the mouse at the time of the event, in the
 }
 
 @defmethod[(get-y)
-           (and/c exact? integer?)]{
+           exact-integer?]{
 
 Returns the y-position of the mouse at the time of the event in the
  target's window's (client-area) coordinate system.
@@ -371,7 +371,7 @@ Sets whether the Shift key was down for the event.
 
 }
 
-@defmethod[(set-x [pos (and/c exact? integer?)])
+@defmethod[(set-x [pos exact-integer?])
            void?]{
 
 Sets the x-position of the mouse at the time of the event in the
@@ -379,7 +379,7 @@ Sets the x-position of the mouse at the time of the event in the
 
 }
 
-@defmethod[(set-y [pos (and/c exact? integer?)])
+@defmethod[(set-y [pos exact-integer?])
            void?]{
 
 Sets the y-position of the mouse at the time of the event in the
diff --git a/collects/scribblings/gui/mouse-event-class.scrbl b/collects/scribblings/gui/mouse-event-class.scrbl
index e050d77d9f..4ba715b867 100644
--- a/collects/scribblings/gui/mouse-event-class.scrbl
+++ b/collects/scribblings/gui/mouse-event-class.scrbl
@@ -19,13 +19,13 @@ See also @|mousekeydiscuss|.
                  [left-down any/c #f]
                  [middle-down any/c #f]
                  [right-down any/c #f]
-                 [x (and/c exact? integer?) 0]
-                 [y (and/c exact? integer?) 0]
+                 [x exact-integer? 0]
+                 [y exact-integer? 0]
                  [shift-down any/c #f]
                  [control-down any/c #f]
                  [meta-down any/c #f]
                  [alt-down any/c #f]
-                 [time-stamp (and/c exact? integer?) 0]
+                 [time-stamp exact-integer? 0]
                  [caps-down any/c #f])]{
 
 Creates a mouse event for a particular type of event. The event types
@@ -192,7 +192,7 @@ Returns @scheme[#t] if the Shift key was down for the event.
 }
 
 @defmethod[(get-x)
-           (and/c exact? integer?)]{
+           exact-integer?]{
 
 Returns the x-position of the mouse at the time of the event, in the
  target's window's (client-area) coordinate system.
@@ -200,7 +200,7 @@ Returns the x-position of the mouse at the time of the event, in the
 }
 
 @defmethod[(get-y)
-           (and/c exact? integer?)]{
+           exact-integer?]{
 
 Returns the y-position of the mouse at the time of the event in the
  target's window's (client-area) coordinate system.
@@ -304,7 +304,7 @@ Sets whether the Shift key was down for the event.
 
 }
 
-@defmethod[(set-x [pos (and/c exact? integer?)])
+@defmethod[(set-x [pos exact-integer?])
            void?]{
 
 Sets the x-position of the mouse at the time of the event in the
@@ -312,7 +312,7 @@ Sets the x-position of the mouse at the time of the event in the
 
 }
 
-@defmethod[(set-y [pos (and/c exact? integer?)])
+@defmethod[(set-y [pos exact-integer?])
            void?]{
 
 Sets the y-position of the mouse at the time of the event in the
diff --git a/collects/scribblings/gui/pasteboard-class.scrbl b/collects/scribblings/gui/pasteboard-class.scrbl
index 5c109bb628..0be1c6a0fc 100644
--- a/collects/scribblings/gui/pasteboard-class.scrbl
+++ b/collects/scribblings/gui/pasteboard-class.scrbl
@@ -500,7 +500,7 @@ Deletes @scheme[snip] when provided, or deletes the currently selected
 
 
 @defmethod[#:mode override 
-           (do-copy [time (and/c exact? integer?)]
+           (do-copy [time exact-integer?]
                     [extend? any/c])
            void?]{
 
@@ -525,7 +525,7 @@ Copies the current selection, extending the current clipboard contexts
 
 
 @defmethod[#:mode override
-           (do-paste [time (and/c exact? integer?)])
+           (do-paste [time exact-integer?])
            void?]{
 @methspec{
 
@@ -547,7 +547,7 @@ Pastes.
 
 
 @defmethod[#:mode override
-           (do-paste-x-selection [time (and/c exact? integer?)])
+           (do-paste-x-selection [time exact-integer?])
            void?]{
 @methspec{
 
diff --git a/collects/scribblings/gui/scroll-event-class.scrbl b/collects/scribblings/gui/scroll-event-class.scrbl
index 26a8dbae7b..db4666e6a4 100644
--- a/collects/scribblings/gui/scroll-event-class.scrbl
+++ b/collects/scribblings/gui/scroll-event-class.scrbl
@@ -18,7 +18,7 @@ See
                              'thumb]
                  [direction (one-of/c 'horizontal 'vertical) 'vertical]
                  [position (integer-in 0 10000) 0]
-                 [time-stamp (and/c exact? integer?) 0])]{
+                 [time-stamp exact-integer? 0])]{
 
 See the corresponding @scheme[get-] and @scheme[set-] methods for
  information about @scheme[event-type], @scheme[direction], @scheme[position],
diff --git a/collects/scribblings/gui/snip-class-class.scrbl b/collects/scribblings/gui/snip-class-class.scrbl
index 88880800c7..aec01e6a3b 100644
--- a/collects/scribblings/gui/snip-class-class.scrbl
+++ b/collects/scribblings/gui/snip-class-class.scrbl
@@ -51,7 +51,7 @@ A snip class name should usually have the form @scheme["((lib ...)
 }
 
 @defmethod[(get-version)
-           (and/c exact? integer?)]{
+           exact-integer?]{
 
 Returns the version of this snip class. When attempting to load a file
  containing a snip with the same class name but a different version,
@@ -98,7 +98,7 @@ Returns @scheme[#t].
 
 
 @defmethod[(reading-version [stream (is-a?/c editor-stream-in%)])
-           (and/c exact? integer?)]{
+           exact-integer?]{
 
 Returns the version number specified for this snip class for snips
  currently being read from the given stream.
@@ -114,7 +114,7 @@ Sets the class's name. See also @method[snip-class% get-classname].
 }
 
 
-@defmethod[(set-version [v (and/c exact? integer?)])
+@defmethod[(set-version [v exact-integer?])
            void?]{
 
 Sets the version of this class. See @method[snip-class% get-version].
diff --git a/collects/scribblings/gui/snip-class.scrbl b/collects/scribblings/gui/snip-class.scrbl
index efe1e6f1eb..3157418e49 100644
--- a/collects/scribblings/gui/snip-class.scrbl
+++ b/collects/scribblings/gui/snip-class.scrbl
@@ -151,7 +151,7 @@ Creates and returns a copy of this snip. The @method[snip% copy]
                                             'insert-text-box 'insert-pasteboard-box 
                                             'insert-image)]
                               [recursive? any/c #t]
-                              [time (and/c exact? integer?) 0])
+                              [time exact-integer? 0])
            void?]{
 
 See @xmethod[editor<%> do-edit-operation].
diff --git a/collects/scribblings/gui/text-class.scrbl b/collects/scribblings/gui/text-class.scrbl
index caa007f0dc..1e90a6d74f 100644
--- a/collects/scribblings/gui/text-class.scrbl
+++ b/collects/scribblings/gui/text-class.scrbl
@@ -351,7 +351,7 @@ When @scheme[style] is provided: @InStyleListNote[@scheme[style]]
 
 @defmethod[#:mode extend
            (copy [extend? any/c #f]
-                 [time (and/c exact? integer?) 0]
+                 [time exact-integer? 0]
                  [start (or/c exact-nonnegative-integer? 'start) 'start]
                  [end (or/c exact-nonnegative-integer? 'end) 'end])
            void?]{
@@ -382,7 +382,7 @@ In addition to the default @xmethod[editor<%> copy-self-to] work,
 
 @defmethod[#:mode override
            (cut [extend? any/c #f]
-                [time (and/c exact? integer?) 0]
+                [time exact-integer? 0]
                 [start (or/c exact-nonnegative-integer? 'start) 'start]
                 [end (or/c exact-nonnegative-integer? 'end) 'end])
            void?]{
@@ -425,7 +425,7 @@ Deletes the specified range or the currently selected text (when no
 @defmethod[#:mode override
            (do-copy [start exact-nonnegative-integer?]
                     [end exact-nonnegative-integer?]
-                    [time (and/c exact? integer?)]
+                    [time exact-integer?]
                     [extend? any/c])
            void?]{
 @methspec{
@@ -449,7 +449,7 @@ Copy the data from @scheme[start] to @scheme[end], extending the current
 
 @defmethod[#:mode override
            (do-paste [start exact-nonnegative-integer?]
-                     [time (and/c exact? integer?)])
+                     [time exact-integer?])
            void?]{
 @methspec{
 
@@ -471,7 +471,7 @@ Pastes into the @techlink{position} @scheme[start].
 
 @defmethod[#:mode override
            (do-paste-x-selection [start exact-nonnegative-integer?]
-                                 [time (and/c exact? integer?)])
+                                 [time exact-integer?])
            void?]{
 @methspec{
 
@@ -1112,9 +1112,9 @@ See also @method[text% get-styles-sticky].
 
 
 @defmethod*[#:mode override
-            ([(kill [time (and/c exact? integer?) 0])
+            ([(kill [time exact-integer? 0])
               void?]
-             [(kill [time (and/c exact? integer?)]
+             [(kill [time exact-integer?]
                     [start exact-nonnegative-integer?]
                     [end exact-nonnegative-integer?])
               void?])]{
@@ -1563,7 +1563,7 @@ If the paragraph starts with invisible @techlink{item}s and @scheme[visible?] is
 
 
 @defmethod[#:mode override
-           (paste [time (and/c exact? integer?) 0]
+           (paste [time exact-integer? 0]
                   [start (or/c exact-nonnegative-integer? 'start 'end) 'start]
                   [end (or/c exact-nonnegative-integer? 'same) 'same])
            void?]{
@@ -1605,7 +1605,7 @@ If the previous operation on the editor was not a paste, calling
 
 
 @defmethod[#:mode override
-           (paste-x-selection [time (and/c exact? integer?)]
+           (paste-x-selection [time exact-integer?]
                               [start (or/c exact-nonnegative-integer? 'start 'end) 'start]
                               [end (or/c exact-nonnegative-integer? 'same) 'same])
            void?]{