diff --git a/t/all.do b/t/all.do
index f1831e0..4e9f6bb 100644
--- a/t/all.do
+++ b/t/all.do
@@ -6,13 +6,26 @@ if [ "$(cat 000-set-minus-e/log)" != "ok" ]; then
     exit 5
 fi
 
-# builds 1xx*/all
+# builds 1xx*/all to test for basic/dangerous functionality.
+# We don't want to run more advanced tests if the basics don't work.
 /bin/ls 1[0-9][0-9]*/all.do |
 sed 's/\.do$//' |
 xargs redo
 110-compile/hello >&2
 
-# builds the rest
+# builds most of the rest in parallel
 /bin/ls [2-9][0-9][0-9]*/all.do |
 sed 's/\.do$//' |
 xargs redo
+
+# builds the tests that require non-parallel execution.
+# If tests are written carefully, this should only be things that
+# are checking for unnecessary extra rebuilds of some targets, which
+# might happen after flush-cache.
+# FIXME: a better solution might be to make flush-cache less destructive!
+/bin/ls [s][0-9][0-9]*/all.do |
+sed 's/\.do$//' | {
+    while read d; do
+        redo "$d"
+    done
+}
diff --git a/t/660-stamp/.gitignore b/t/s60-stamp/.gitignore
similarity index 100%
rename from t/660-stamp/.gitignore
rename to t/s60-stamp/.gitignore
diff --git a/t/660-stamp/a.do b/t/s60-stamp/a.do
similarity index 100%
rename from t/660-stamp/a.do
rename to t/s60-stamp/a.do
diff --git a/t/660-stamp/ab.do b/t/s60-stamp/ab.do
similarity index 100%
rename from t/660-stamp/ab.do
rename to t/s60-stamp/ab.do
diff --git a/t/660-stamp/abc.do b/t/s60-stamp/abc.do
similarity index 100%
rename from t/660-stamp/abc.do
rename to t/s60-stamp/abc.do
diff --git a/t/660-stamp/all.do b/t/s60-stamp/all.do
similarity index 100%
rename from t/660-stamp/all.do
rename to t/s60-stamp/all.do
diff --git a/t/660-stamp/b.do b/t/s60-stamp/b.do
similarity index 100%
rename from t/660-stamp/b.do
rename to t/s60-stamp/b.do
diff --git a/t/660-stamp/bob.do b/t/s60-stamp/bob.do
similarity index 100%
rename from t/660-stamp/bob.do
rename to t/s60-stamp/bob.do
diff --git a/t/660-stamp/c b/t/s60-stamp/c
similarity index 100%
rename from t/660-stamp/c
rename to t/s60-stamp/c
diff --git a/t/660-stamp/clean.do b/t/s60-stamp/clean.do
similarity index 100%
rename from t/660-stamp/clean.do
rename to t/s60-stamp/clean.do
diff --git a/t/660-stamp/stamptest.do b/t/s60-stamp/stamptest.do
similarity index 97%
rename from t/660-stamp/stamptest.do
rename to t/s60-stamp/stamptest.do
index 6e318ed..d8a6b84 100644
--- a/t/660-stamp/stamptest.do
+++ b/t/s60-stamp/stamptest.do
@@ -1,4 +1,4 @@
-rm -f stampy usestamp usestamp2 stampy.log usestamp.log usestamp2.log
+rm -f bob stampy usestamp usestamp2 stampy.log usestamp.log usestamp2.log
 echo one >inp
 
 ../flush-cache
diff --git a/t/660-stamp/stampy.do b/t/s60-stamp/stampy.do
similarity index 68%
rename from t/660-stamp/stampy.do
rename to t/s60-stamp/stampy.do
index 96816c4..cc22014 100644
--- a/t/660-stamp/stampy.do
+++ b/t/s60-stamp/stampy.do
@@ -2,4 +2,4 @@ echo $$ >>stampy.log
 redo-ifchange inp bob
 cat inp
 cd ..
-redo-stamp <660-stamp/inp
+redo-stamp <s60-stamp/inp
diff --git a/t/660-stamp/usestamp.do b/t/s60-stamp/usestamp.do
similarity index 100%
rename from t/660-stamp/usestamp.do
rename to t/s60-stamp/usestamp.do
diff --git a/t/660-stamp/usestamp2.do b/t/s60-stamp/usestamp2.do
similarity index 100%
rename from t/660-stamp/usestamp2.do
rename to t/s60-stamp/usestamp2.do