diff --git a/tests/docker/Makefile.include b/tests/docker/Makefile.include
index 59dd8e314d..a2dd307a8e 100644
--- a/tests/docker/Makefile.include
+++ b/tests/docker/Makefile.include
@@ -73,6 +73,7 @@ docker-image-debian-sid: NOCACHE=1
 docker-image-debian-alpha-cross: docker-image-debian-sid
 docker-image-debian-hppa-cross: docker-image-debian-sid
 docker-image-debian-m68k-cross: docker-image-debian-sid
+docker-image-debian-sh4-cross: docker-image-debian-sid
 docker-image-travis: NOUSER=1
 
 # Specialist build images, sometimes very limited tools
diff --git a/tests/docker/dockerfiles/debian-sh4-cross.docker b/tests/docker/dockerfiles/debian-sh4-cross.docker
new file mode 100644
index 0000000000..88a2423094
--- /dev/null
+++ b/tests/docker/dockerfiles/debian-sh4-cross.docker
@@ -0,0 +1,12 @@
+#
+# Docker cross-compiler target
+#
+# This docker target builds on the debian sid base image which
+# contains cross compilers for Debian "ports" targets.
+#
+FROM qemu:debian-sid
+
+RUN DEBIAN_FRONTEND=noninteractive eatmydata \
+    apt-get install -y --no-install-recommends \
+        gcc-sh4-linux-gnu \
+        libc6-dev-sh4-cross
diff --git a/tests/tcg/sh4/Makefile.include b/tests/tcg/sh4/Makefile.include
new file mode 100644
index 0000000000..ad21594d9d
--- /dev/null
+++ b/tests/tcg/sh4/Makefile.include
@@ -0,0 +1,4 @@
+ifneq ($(TARGET_NAME), sh4eb)
+DOCKER_IMAGE=debian-sh4-cross
+DOCKER_CROSS_COMPILER=sh4-linux-gnu-gcc
+endif
diff --git a/tests/tcg/sh4/Makefile.target b/tests/tcg/sh4/Makefile.target
new file mode 100644
index 0000000000..9d18d44612
--- /dev/null
+++ b/tests/tcg/sh4/Makefile.target
@@ -0,0 +1,7 @@
+# -*- Mode: makefile -*-
+#
+# SuperH specific tweaks
+#
+
+# On sh Linux supports 4k, 8k, 16k and 64k pages (but only 4k currently works)
+EXTRA_RUNS+=run-test-mmap-4096 # run-test-mmap-8192 run-test-mmap-16384 run-test-mmap-65536