diff --git a/.github/workflows/validate.yml b/.github/workflows/validate.yml
index 146d769f4..02e3228f2 100644
--- a/.github/workflows/validate.yml
+++ b/.github/workflows/validate.yml
@@ -98,3 +98,22 @@ jobs:
           commits: ${{ steps.get-pr-commits.outputs.commits }}
           pattern: '^.{0,72}(\n.*)*$'
           error: 'Subject too long (max 72)'
+
+
+  cross:
+    runs-on: ubuntu-20.04
+    steps:
+    - uses: actions/checkout@v2
+      # We have to run this under Docker as Ubuntu (host) does not support all
+      # the architectures we want to compile test against, and Dockerfile uses
+      # Debian (which does).
+      #
+      # XXX: as currently this is the only job that is using Docker, we are
+      # building and using the runcimage locally. In case more jobs running
+      # under Docker will emerge, it will be good to have a separate make
+      # runcimage job and share its result (the docker image) with whoever
+      # needs it.
+    - name: build docker image
+      run: make runcimage
+    - name: cross
+      run: make cross
diff --git a/.travis.yml b/.travis.yml
index 597c59007..bbb34594e 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -65,4 +65,4 @@ before_install:
 
 script:
   - make
-  - make clean ci cross
+  - make clean ci
diff --git a/Dockerfile b/Dockerfile
index bb22f4d8f..1b38390ea 100644
--- a/Dockerfile
+++ b/Dockerfile
@@ -60,9 +60,7 @@ ARG UMOCI_VERSION
 RUN curl -o /usr/local/bin/umoci -fsSL https://github.com/opencontainers/umoci/releases/download/${UMOCI_VERSION}/umoci.amd64 \
     && chmod +x /usr/local/bin/umoci
 
-COPY script/tmpmount /
 WORKDIR /go/src/github.com/opencontainers/runc
-ENTRYPOINT ["/tmpmount"]
 
 # setup a playground for us to spawn containers in
 COPY tests/integration/multi-arch.bash tests/integration/
diff --git a/script/tmpmount b/script/tmpmount
deleted file mode 100755
index 5ac6bc2bf..000000000
--- a/script/tmpmount
+++ /dev/null
@@ -1,4 +0,0 @@
-#!/bin/bash
-
-mount -t tmpfs none /tmp
-exec "$@"