diff --git a/.appveyor.yml b/.appveyor.yml
index 7e08602fe3..7841b963ff 100644
--- a/.appveyor.yml
+++ b/.appveyor.yml
@@ -97,7 +97,7 @@ test_script:
             Set-Location "${env:build}"
             Copy-Item "C:/msys64/${env:compiler_path}/bin/libssp-0.dll" -Destination "${env:build}/src/test"
             Copy-Item "C:/msys64/${env:compiler_path}/bin/zlib1.dll" -Destination "${env:build}/src/test"
-            Execute-Bash "VERBOSE=1 make -k -j2 check"
+            Execute-Bash "VERBOSE=1 TOR_SKIP_TESTCASES=crypto/openssl_version make -k -j2 check"
     }
 
 on_finish:
diff --git a/changes/ticket33643 b/changes/ticket33643
new file mode 100644
index 0000000000..7fddab74eb
--- /dev/null
+++ b/changes/ticket33643
@@ -0,0 +1,5 @@
+  o Minor features (testing):
+    - The unit tests now support a "TOR_SKIP_TESTCASES" environment variable
+      to specify a list of space-separated test cases that should not be
+      executed. We will use this to disable certain tests that are failing on
+      Appveyor because of mismatched OpenSSL libraries. Part of ticket 33643.
diff --git a/changes/ticket33643_part2 b/changes/ticket33643_part2
new file mode 100644
index 0000000000..28193d2af5
--- /dev/null
+++ b/changes/ticket33643_part2
@@ -0,0 +1,3 @@
+  o Testing (CI):
+    - On appveyor, skip the crypto/openssl_version test, which is failing
+      because of a mismatched library installation. Fix for 33643.
diff --git a/src/test/testing_common.c b/src/test/testing_common.c
index ff6028ddb4..06a6f312ad 100644
--- a/src/test/testing_common.c
+++ b/src/test/testing_common.c
@@ -343,6 +343,21 @@ main(int c, const char **v)
 
   atexit(remove_directory);
 
+  /* Look for TOR_SKIP_TESTCASES: a space-separated list of tests to skip. */
+  const char *skip_tests = getenv("TOR_SKIP_TESTCASES");
+  if (skip_tests) {
+    smartlist_t *skip = smartlist_new();
+    smartlist_split_string(skip, skip_tests, NULL,
+                           SPLIT_IGNORE_BLANK, -1);
+    int n = 0;
+    SMARTLIST_FOREACH_BEGIN(skip, char *, cp) {
+      n += tinytest_skip(testgroups, cp);
+      tor_free(cp);
+    } SMARTLIST_FOREACH_END(cp);
+    printf("Skipping %d testcases.\n", n);
+    smartlist_free(skip);
+  }
+
   int have_failed = (tinytest_main(c, v, testgroups) != 0);
 
   free_pregenerated_keys();