diff --git a/Makefile b/Makefile
index fc4a521..13a9d60 100644
--- a/Makefile
+++ b/Makefile
@@ -70,6 +70,10 @@ docker-check-stress:
 docker-bench:
 	$(DOCKER_RUN) sh -c 'make clean && make bench'
 
+docker-valgrind:
+	$(DOCKER_RUN) sh -c 'make clean && make -C tests unit_test && \
+		cd tests && valgrind -q --error-exitcode=1 ./unit_test $(UNITARGS)'
+
 docker: docker-image
 	$(MAKE) docker-build
 
@@ -95,4 +99,4 @@ verify-map:
 
 .PHONY: all check check-live check-stress test verify-map clean gtk bench \
 	docker docker-image docker-build docker-check docker-check-live \
-	docker-check-stress docker-bench
+	docker-check-stress docker-bench docker-valgrind
diff --git a/README.md b/README.md
index ec02c81..b437548 100644
--- a/README.md
+++ b/README.md
@@ -76,8 +76,9 @@ make check-stress   # randomized, capacity, collision, failure, and restart test
 
 `UNITARGS` filters only the focused C unit suite, for example
 `make check UNITARGS=hangul`. It does not select or skip live and stress
-tests. `make docker-check` force-rebuilds and runs all three tiers in the
-container; run `make docker-image` first after changing `Dockerfile`.
+tests. `make docker-check` rebuilds and runs all three tiers in the
+container, and `make docker-valgrind` runs the unit suite under Valgrind
+there; run `make docker-image` first after changing `Dockerfile`.
 
 Native Linux source builds require a C toolchain, Make, pkg-config, Python 3,
 and cmp/diff, plus development files for: