diff --git a/pkgs/racket-pkgs/racket-test/tests/pkg/test.rkt b/pkgs/racket-pkgs/racket-test/tests/pkg/test.rkt
index 4a5385cf80..eb1b7d1a19 100644
--- a/pkgs/racket-pkgs/racket-test/tests/pkg/test.rkt
+++ b/pkgs/racket-pkgs/racket-test/tests/pkg/test.rkt
@@ -50,4 +50,5 @@
  "platform"
  "raco"
  "binary"
- "catalogs")
+ "catalogs"
+ "failure")
diff --git a/pkgs/racket-pkgs/racket-test/tests/pkg/tests-failure.rkt b/pkgs/racket-pkgs/racket-test/tests/pkg/tests-failure.rkt
new file mode 100644
index 0000000000..b03ff3600e
--- /dev/null
+++ b/pkgs/racket-pkgs/racket-test/tests/pkg/tests-failure.rkt
@@ -0,0 +1,36 @@
+#lang racket/base
+(require rackunit
+         racket/system
+         pkg/util
+         "shelly.rkt"
+         "util.rkt")
+
+(pkg-tests
+ (shelly-begin
+  (initialize-catalogs)
+  
+  (with-fake-root
+   (shelly-case
+    "failure on remove"
+    $ "raco pkg install test-pkgs/pkg-test1.zip" =exit> 0
+    $ "raco pkg show -u -a -d" =stdout> #rx"Package\\[\\*=auto\\] +Checksum +Source +Directory\npkg-test1 +[a-f0-9]+ .*pkg-test1\n"
+    $ "racket -e '(require pkg-test1)'" =exit> 0
+    $ "racket -e '(file-or-directory-permissions (collection-path \"pkg-test1\") #o500)'"
+    $ "raco pkg remove pkg-test1" =exit> 1
+    $ "racket -e '(require pkg-test1)'" =exit> 1)
+
+   (shelly-case
+    "re-install must go to \"+1\""
+    $ "raco pkg install test-pkgs/pkg-test1.zip" =exit> 0
+    $ "raco pkg show -u -a -d" =stdout> #rx"Package\\[\\*=auto\\] +Checksum +Source +Directory\npkg-test1 +[a-f0-9]+ .*pkg-test1[+]1\n"
+    $ "racket -e '(require pkg-test1)'" =exit> 0
+    $ "raco pkg remove pkg-test1" =exit> 0
+    $ "racket -e '(require pkg-test1)'" =exit> 1)
+
+   (shelly-case
+    "re-install can go back to original place"
+    $ "racket -l racket/base -l setup/dirs -e '(file-or-directory-permissions (build-path (find-user-pkgs-dir) \"pkg-test1/pkg-test1\") #o700)'"
+    $ "raco pkg install test-pkgs/pkg-test1.zip" =exit> 0
+    $ "raco pkg show -u -a -d" =stdout> #rx"Package\\[\\*=auto\\] +Checksum +Source +Directory\npkg-test1 +[a-f0-9]+ .*pkg-test1\n"
+    $ "racket -e '(require pkg-test1)'" =exit> 0
+    $ "raco pkg remove pkg-test1" =exit> 0))))
diff --git a/racket/collects/pkg/lib.rkt b/racket/collects/pkg/lib.rkt
index 96453a63af..d06083e49c 100644
--- a/racket/collects/pkg/lib.rkt
+++ b/racket/collects/pkg/lib.rkt
@@ -658,14 +658,34 @@
            [`(,(or 'link 'static-link) ,orig-pkg-dir)
             (path->complete-path orig-pkg-dir (pkg-installed-dir))]
            [_
-            (build-path (pkg-installed-dir) pkg-name)]))))
+            (build-path (pkg-installed-dir) 
+                        (or (cond
+                             [(pkg-info/alt? info)
+                              (pkg-info/alt-dir-name info)]
+                             [(sc-pkg-info/alt? info)
+                              (sc-pkg-info/alt-dir-name info)]
+                             [else #f])
+                            pkg-name))]))))
+
+(define (make-pkg-info orig-pkg checksum auto? single-collect alt-dir-name)
+  ;; Picks the right structure subtype
+  (if single-collect
+      (if alt-dir-name
+          (sc-pkg-info/alt orig-pkg checksum auto? single-collect alt-dir-name)
+          (sc-pkg-info orig-pkg checksum auto? single-collect))
+      (if alt-dir-name
+          (pkg-info/alt orig-pkg checksum auto? alt-dir-name)
+          (pkg-info orig-pkg checksum auto?))))
 
 (define (update-auto this-pkg-info auto?)
   (match-define (pkg-info orig-pkg checksum _) this-pkg-info)
-  (if (sc-pkg-info? this-pkg-info)
-      (sc-pkg-info orig-pkg checksum auto?
-                   (sc-pkg-info-collect this-pkg-info))
-      (pkg-info orig-pkg checksum auto?)))
+  (make-pkg-info orig-pkg checksum auto?
+                 (and (sc-pkg-info? this-pkg-info)
+                      (sc-pkg-info-collect this-pkg-info))
+                 (or (and (sc-pkg-info/alt? this-pkg-info)
+                          (sc-pkg-info/alt-dir-name this-pkg-info))
+                     (and (pkg-info/alt? this-pkg-info)
+                          (pkg-info/alt-dir-name this-pkg-info)))))
 
 (define (demote-packages quiet? pkg-names)
   (define db (read-pkg-db))
@@ -1567,7 +1587,8 @@
          (define final-pkg-dir
            (cond
              [clean?
-              (define final-pkg-dir (build-path (pkg-installed-dir) pkg-name))
+              (define final-pkg-dir (select-package-directory
+                                     (build-path (pkg-installed-dir) pkg-name)))
               (make-parent-directory* final-pkg-dir)
               (copy-directory/files pkg-dir final-pkg-dir #:keep-modify-seconds? #t)
               (clean!)
@@ -1589,10 +1610,13 @@
                 #:root? (not single-collect)
                 #:static-root? (and (pair? orig-pkg)
                                     (eq? 'static-link (car orig-pkg))))
+         (define alt-dir-name
+           ;; If we had to pick an alternate dir name, then record it:
+           (let-values ([(base name dir?) (split-path final-pkg-dir)])
+             (and (regexp-match? #rx"[+]" name)
+                  (path->string name))))
          (define this-pkg-info
-           (if single-collect
-               (sc-pkg-info orig-pkg checksum auto? single-collect)
-               (pkg-info orig-pkg checksum auto?)))
+           (make-pkg-info orig-pkg checksum auto? single-collect alt-dir-name))
          (log-pkg-debug "updating db with ~e to ~e" pkg-name this-pkg-info)
          (update-pkg-db! pkg-name this-pkg-info))]))
   (define metadata-ns (make-metadata-namespace))
@@ -1730,6 +1754,35 @@
       (loop new-check
             (set-union setup-pkgs new-check))])))
 
+(define (select-package-directory dir #:counter [counter 0])
+  (define full-dir (if (zero? counter)
+                       dir
+                       (let-values ([(base name dir?) (split-path dir)])
+                         (define new-name (bytes->path
+                                           (bytes-append (path->bytes name)
+                                                         (string->bytes/utf-8
+                                                          (~a "+" counter)))))
+                         (if (path? base)
+                             (build-path base new-name)
+                             new-name))))
+  (cond
+   [(directory-exists? full-dir)
+    ;; If the directory exists, assume that we'd like to replace it.
+    ;; Maybe the directory couldn't be deleted when a package was
+    ;; uninstalled, and maybe it will work now (because some process
+    ;; has completed on Windows or some other filesystem with locks).
+    (with-handlers ([exn:fail:filesystem?
+                     (lambda (exn)
+                       (log-pkg-warning "error deleting old directory: ~a" 
+                                        (exn-message exn))
+                       (select-package-directory dir #:counter (add1 counter)))])
+      (delete-directory/files full-dir)
+      ;; delete succeeded:
+      full-dir)]
+   [else
+    ;; all clear to use the selected name:
+    full-dir]))
+
 (define (snoc l x)
   (append l (list x)))
 
diff --git a/racket/collects/pkg/path.rkt b/racket/collects/pkg/path.rkt
index 3d0b7deb72..41233719fc 100644
--- a/racket/collects/pkg/path.rkt
+++ b/racket/collects/pkg/path.rkt
@@ -2,7 +2,9 @@
 (require setup/dirs)
 
 (provide (struct-out pkg-info)
+         (struct-out pkg-info/alt)
          (struct-out sc-pkg-info)
+         (struct-out sc-pkg-info/alt)
          get-pkgs-dir
          read-pkgs-db
          read-pkg-file-hash
@@ -11,7 +13,9 @@
          path->pkg+subpath+collect)
 
 (struct pkg-info (orig-pkg checksum auto?) #:prefab)
+(struct pkg-info/alt pkg-info (dir-name) #:prefab) ; alternate installation directory
 (struct sc-pkg-info pkg-info (collect) #:prefab) ; a pkg with a single collection
+(struct sc-pkg-info/alt sc-pkg-info (dir-name) #:prefab) ; alternate installation
 
 (define (check-scope who scope)
   (unless (or (eq? scope 'user)
@@ -103,10 +107,13 @@
      [(sub-path? < p d)
       ;; Under the installation mode's package directory.
       ;; We assume that no one else writes there, so the
-      ;; next path element is the package name.
+      ;; next path element is the package name (or the package
+      ;; name followed by "+<n>")
       (define len (length d))
       (define pkg-name (path-element->string (list-ref p len)))
-      (values pkg-name
+      (values (if (regexp-match? #rx"[+]" pkg-name) ; +<n> used as an alternate path, sometimes
+                  (regexp-replace #rx"[+].*$" pkg-name "")
+                  pkg-name)
               (build-path* (list-tail p (add1 len)))
               (and want-collect?
                    (let ([i (hash-ref (read-pkg-db/cached) pkg-name #f)])