diff --git a/Dockerfile b/Dockerfile
index a84a860..33c753b 100644
--- a/Dockerfile
+++ b/Dockerfile
@@ -42,20 +42,35 @@ RUN go mod tidy -diff || \
 # Go's build cache is kept on a tmpfs, out of the image: nothing uses it
 # after this step, and writing it into the image takes seconds. The tests
 # are built with the no_fs_access tag, as the binary is in the build stage.
+#
+# The race detector finds bugs only in code that runs in several goroutines
+# at once. Of the Core Rule Set's tests, only
+# TestConcurrentRequestsKeepTheirOwnExclusions inspects requests that way,
+# so it is the only one of them in this pass. The second pass runs the rest.
 FROM test-setup AS test-race
 
 RUN --mount=type=tmpfs,target=/root/.cache/go-build \
-    go test -tags no_fs_access -timeout 90s -race -cover ./... || \
+    others="$(go list ./... | grep -vxF sneak.berlin/go/smallwebwaf/internal/coreruleset)"; \
+    { go test -tags no_fs_access -timeout 90s -race -cover $others && \
+      go test -tags no_fs_access -timeout 90s -race -cover \
+        -run '^TestConcurrentRequestsKeepTheirOwnExclusions$' ./internal/coreruleset; } || \
     { echo "--- Rerunning with -v for details ---"; \
-      go test -tags no_fs_access -timeout 90s -race -v ./...; exit 1; }
+      go test -tags no_fs_access -timeout 90s -race -v $others; \
+      go test -tags no_fs_access -timeout 90s -race -v \
+        -run '^TestConcurrentRequestsKeepTheirOwnExclusions$' ./internal/coreruleset; \
+      exit 1; }
 
-# Second pass: the recorded requests, too slow for make test under -race.
+# Second pass: every other test of the Core Rule Set, the recorded requests
+# among them, without the race detector.
 FROM test-setup AS test-recorded
 
 RUN --mount=type=tmpfs,target=/root/.cache/go-build \
-    go test -tags no_fs_access,recorded -timeout 90s -cover -run '^TestOrdinary' ./internal/coreruleset/... || \
+    go test -tags no_fs_access,recorded -timeout 90s -cover \
+        -skip '^TestConcurrentRequestsKeepTheirOwnExclusions$' ./internal/coreruleset || \
     { echo "--- Rerunning with -v for details ---"; \
-      go test -tags no_fs_access,recorded -timeout 90s -run '^TestOrdinary' -v ./internal/coreruleset/...; exit 1; }
+      go test -tags no_fs_access,recorded -timeout 90s -v \
+        -skip '^TestConcurrentRequestsKeepTheirOwnExclusions$' ./internal/coreruleset; \
+      exit 1; }
 
 # The test phase that script/test and the build stage name. Nothing is
 # wanted from the two passes; the copies are what make BuildKit run them.
diff --git a/README.md b/README.md
index 7f8d919..5f400d6 100644
--- a/README.md
+++ b/README.md
@@ -702,8 +702,12 @@ on the host.
 - `script/projectname`: prints `smallwebwaf`, which the other scripts tag their
   images with.
 - `script/test`: checks that `go.mod` and `go.sum` are tidy, then runs the
-  tests, as the `test` phase of the `Dockerfile`. It runs them twice: once with
-  the race detector, and once without it for the recorded requests. `make test`.
+  tests, as the `test` phase of the `Dockerfile`, in two passes. `make test`.
+    - The first runs every package's tests with the race detector. Of the Core
+      Rule Set's tests, it runs only the one that inspects requests from several
+      goroutines at once.
+    - The second runs the Core Rule Set's other tests without the race detector,
+      the recorded requests among them.
 - `script/tidy`: writes `go.mod` and `go.sum` as `go mod tidy` writes them, in
   the `tidy` stage of the `Dockerfile`. `make tidy`.
 - `script/lint`: runs golangci-lint, as the `lint` phase of the `Dockerfile`.