diff --git a/tests/docker/Makefile.include b/tests/docker/Makefile.include
index b2a7e761cc..09fb7db7fa 100644
--- a/tests/docker/Makefile.include
+++ b/tests/docker/Makefile.include
@@ -6,7 +6,7 @@ DOCKER_SUFFIX := .docker
 DOCKER_FILES_DIR := $(SRC_PATH)/tests/docker/dockerfiles
 DOCKER_DEPRECATED_IMAGES := debian
 # we don't run tests on intermediate images (used as base by another image)
-DOCKER_INTERMEDIATE_IMAGES := debian8 debian9 debian8-mxe debian-ports debian-sid
+DOCKER_PARTIAL_IMAGES := debian debian8 debian9 debian8-mxe debian-ports debian-sid debian-bootstrap
 DOCKER_IMAGES := $(filter-out $(DOCKER_DEPRECATED_IMAGES),$(sort $(notdir $(basename $(wildcard $(DOCKER_FILES_DIR)/*.docker)))))
 DOCKER_TARGETS := $(patsubst %,docker-image-%,$(DOCKER_IMAGES))
 # Use a global constant ccache directory to speed up repetitive builds
@@ -121,6 +121,11 @@ docker-image-travis: NOUSER=1
 # Specialist build images, sometimes very limited tools
 docker-image-tricore-cross: docker-image-debian9
 
+# These images may be good enough for building tests but not for test builds
+DOCKER_PARTIAL_IMAGES += debian-alpha-cross debian-hppa-cross debian-m68k-cross debian-sh4-cross
+DOCKER_PARTIAL_IMAGES += debian-sparc64-cross debian-mips64-cross debian-riscv64-cross
+DOCKER_PARTIAL_IMAGES += debian-tricore-cross debian-powerpc-cross fedora-i386-cross
+
 # Rules for building linux-user powered images
 #
 # These are slower than using native cross compiler setups but can
@@ -137,7 +142,7 @@ docker-image-debian-powerpc-user-cross: docker-binfmt-image-debian-powerpc-user
 DOCKER_USER_IMAGES += debian-powerpc-user
 
 # Expand all the pre-requistes for each docker image and test combination
-$(foreach i,$(filter-out $(DOCKER_INTERMEDIATE_IMAGES),$(DOCKER_IMAGES) $(DOCKER_DEPRECATED_IMAGES)), \
+$(foreach i,$(filter-out $(DOCKER_PARTIAL_IMAGES),$(DOCKER_IMAGES) $(DOCKER_DEPRECATED_IMAGES)), \
 	$(foreach t,$(DOCKER_TESTS) $(DOCKER_TOOLS), \
 		$(eval .PHONY: docker-$t@$i) \
 		$(eval docker-$t@$i: docker-image-$i docker-run-$t@$i) \