diff --git a/collects/tests/r6rs/base.sls b/collects/tests/r6rs/base.sls
index 50bcf669e6..39525229fb 100644
--- a/collects/tests/r6rs/base.sls
+++ b/collects/tests/r6rs/base.sls
@@ -62,11 +62,11 @@
     (syntax-rules ()
       [(_ op)
        (begin
-         (test/exn (op 1 0) &assertion)
-         (test/exn (op 1 0.0) &assertion)
-         (test/exn (op +inf.0 1) &assertion)
-         (test/exn (op -inf.0 1) &assertion)
-         (test/exn (op +nan.0 1) &assertion))]))
+         (test/unspec-flonum-or-exn (op 1 0) &assertion)
+         (test/unspec-flonum-or-exn (op 1 0.0) &assertion)
+         (test/unspec-flonum-or-exn (op +inf.0 1) &assertion)
+         (test/unspec-flonum-or-exn (op -inf.0 1) &assertion)
+         (test/unspec-flonum-or-exn (op +nan.0 1) &assertion))]))
 
   (define-syntax test-string-to-number
     (syntax-rules ()
@@ -924,7 +924,7 @@
     (for-each 
      (lambda (n)
        (test (string->number (number->string n)) n)
-       (test (string->number (number->string n 10 5)) n)
+       (test (string->number (number->string (inexact n) 10 5)) (inexact n))
        (when (exact? n)
          (test (string->number (number->string n 16) 16) n)
          (test (string->number (string-append "#x" (number->string n 16))) n)
diff --git a/collects/tests/r6rs/io/ports.sls b/collects/tests/r6rs/io/ports.sls
index e49a3c8e12..ad12c2191f 100644
--- a/collects/tests/r6rs/io/ports.sls
+++ b/collects/tests/r6rs/io/ports.sls
@@ -342,16 +342,15 @@
       (close-port p))
     (let ([p (open-file-input-port "io-tmp1")])
       (let ([b1 (get-u8 p)])
-        (if (= b1 #xFE)
-            (begin
-              (test (get-u8 p) #xFF)
-              (test (get-u8 p) 0)
-              (test (get-u8 p) 97))
-            (begin
-              (test b1 #xFF)
-              (test (get-u8 p) #xFE)
-              (test (get-u8 p) 97)
-              (test (get-u8 p) 0))))
+        (cond
+        [(equal? b1 #xFE)
+         (test (get-u8 p) #xFF)
+         (test (get-u8 p) 0)
+         (test (get-u8 p) 97)]
+        [(equal? b1 #xFF)
+         (test (get-u8 p) #xFE)
+         (test (get-u8 p) 97)
+         (test (get-u8 p) 0)]))
       (test/unspec (close-port p)))
 
     (let ([bytevector->string-via-file
@@ -566,20 +565,24 @@
                (lambda () pos)
                (lambda (p) (set! pos p))
                (lambda () 'ok))])
-      (test (port-position p) 0)
+      (test/unspec (port-position p))
       (test (get-string-n p 3) "abc")
-      (test (port-position p) 3)
-      (test (lookahead-char p) #\d)
-      (test (lookahead-char p) #\d)
-      (test (port-position p) 3)
-      (test/unspec (set-port-position! p 10))
-      (get-string-n p 2)
-      (test (get-string-n p 2) "mn")
-      (test (get-string-n p 2) "op")
-      (test (get-string-n p 2) (eof-object))
-      (test/unspec (set-port-position! p 2))
-      (test (get-string-n p 3) "cde")
-      (test/unspec (close-port p)))
+      (let ([pos3 (port-position p)])
+        (test (lookahead-char p) #\d)
+        (test (lookahead-char p) #\d)
+        (test (port-position p) pos3)
+        (test (get-string-n p 7) "defghij")
+        (let ([pos10 (port-position p)])
+          (get-string-n p 2)
+          (test (get-string-n p 2) "mn")
+          (test/unspec (set-port-position! p pos10))
+          (get-string-n p 2)
+          (test (get-string-n p 2) "mn"))
+        (test (get-string-n p 2) "op")
+        (test (get-string-n p 2) (eof-object))
+        (test/unspec (set-port-position! p pos3))
+        (test (get-string-n p 3) "def")
+        (test/unspec (close-port p))))
 
     (test-positions make-custom-textual-input-port)
     
diff --git a/collects/tests/r6rs/lists.sls b/collects/tests/r6rs/lists.sls
index 87218cc0e3..91a3b602d5 100644
--- a/collects/tests/r6rs/lists.sls
+++ b/collects/tests/r6rs/lists.sls
@@ -15,7 +15,7 @@
     
     (test (for-all even? '()) #t)
     (test (for-all even? '(3 1 4 1 5 9)) #f)
-    (test (for-all even? '(3 1 4 1 5 9 . 2)) #f)
+    ;; (test (for-all even? '(3 1 4 1 5 9 . 2)) #f) ; removed from R6RS
     (test (for-all even? '(2 4 14)) #t)
     (test/exn (for-all even? '(2 4 14 . 9)) &assertion)
     (test (for-all (lambda (n) (and (even? n) n))
@@ -121,7 +121,7 @@
     (test (for-all (lambda (x) x) '(12 14)) 14)
     (test (for-all (lambda (x) x) '(12)) 12)
     (test (for-all (lambda (x) x) '()) #t)
-    (test (for-all even? '(13 . 14)) #f)
+    ;; (test (for-all even? '(13 . 14)) #f) ; removed from R6RS
     (test (for-all cons '(1 2 3) '(a b c)) '(3 . c))
     (test (for-all (lambda (a b) (= a 1)) '(1 2 3) '(a b c)) #f)
     ;; R6RS merely says that this *should* work, but not must:
diff --git a/collects/tests/r6rs/test.sls b/collects/tests/r6rs/test.sls
index cb9bf479db..19dae25955 100644
--- a/collects/tests/r6rs/test.sls
+++ b/collects/tests/r6rs/test.sls
@@ -9,6 +9,7 @@
           test/output
           test/unspec
           test/unspec-or-exn
+          test/unspec-flonum-or-exn
           test/output/unspec
           run-test
           report-test-results)
@@ -123,6 +124,19 @@
                     (begin expr 'unspec))
              'unspec)]))
 
+  (define-syntax test/unspec-flonum-or-exn
+    (syntax-rules ()
+      [(_ expr condition)
+       (test (guard (c [((condition-predicate (record-type-descriptor condition)) c)
+                        'unspec-or-flonum])
+                    (let ([v expr])
+                      (if (flonum? v)
+                          'unspec-or-flonum
+                          (if (eq? v 'unspec-or-flonum)
+                              (list v)
+                              v))))
+             'unspec-or-flonum)]))
+
   (define-syntax test/output/unspec
     (syntax-rules ()
       [(_ expr str)