diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index ddeb489c647df..5f14cd36ce434 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -382,6 +382,7 @@ jobs:
           - name: x86_64-msvc-ext
             env:
               SCRIPT: python x.py --stage 2 test src/tools/cargotest src/tools/cargo && src/ci/docker/host-x86_64/x86_64-gnu-tools/checktools.sh x.py /tmp/toolstate/toolstates.json windows
+              HOST_TARGET: x86_64-pc-windows-msvc
               RUST_CONFIGURE_ARGS: "--build=x86_64-pc-windows-msvc --enable-lld --save-toolstates=/tmp/toolstate/toolstates.json"
               DEPLOY_TOOLSTATES_JSON: toolstates-windows.json
             os: windows-2019-8core-32gb
diff --git a/src/ci/docker/host-x86_64/x86_64-gnu-tools/Dockerfile b/src/ci/docker/host-x86_64/x86_64-gnu-tools/Dockerfile
index 85f2f84a44c32..b0eeff0c57615 100644
--- a/src/ci/docker/host-x86_64/x86_64-gnu-tools/Dockerfile
+++ b/src/ci/docker/host-x86_64/x86_64-gnu-tools/Dockerfile
@@ -83,6 +83,8 @@ ENV RUST_CONFIGURE_ARGS \
   --build=x86_64-unknown-linux-gnu \
   --save-toolstates=/tmp/toolstate/toolstates.json
 
+ENV HOST_TARGET x86_64-unknown-linux-gnu
+
 ENV SCRIPT /tmp/checktools.sh ../x.py && \
   NODE_PATH=`npm root -g` python3 ../x.py test tests/rustdoc-gui --stage 2 \
     --test-args "'--no-sandbox --jobs 1'"
diff --git a/src/ci/docker/host-x86_64/x86_64-gnu-tools/checktools.sh b/src/ci/docker/host-x86_64/x86_64-gnu-tools/checktools.sh
index 7dde6370904bb..821a09feb2d53 100755
--- a/src/ci/docker/host-x86_64/x86_64-gnu-tools/checktools.sh
+++ b/src/ci/docker/host-x86_64/x86_64-gnu-tools/checktools.sh
@@ -1,4 +1,5 @@
 #!/bin/sh
+# ignore-tidy-linelength
 
 set -eu
 
@@ -26,8 +27,30 @@ python3 "$X_PY" test --stage 2 src/tools/clippy
 python3 "$X_PY" test --stage 2 src/tools/rustfmt
 python3 "$X_PY" test --stage 2 src/tools/miri
 # We natively run this script on x86_64-unknown-linux-gnu and x86_64-pc-windows-msvc.
-# Also cover some other targets (on both of these hosts) via cross-testing.
+# Also cover some other targets via cross-testing, in particular all tier 1 targets.
 export BOOTSTRAP_SKIP_TARGET_SANITY=1 # we don't need `cc` for these targets
-python3 "$X_PY" test --stage 2 src/tools/miri --target i686-pc-windows-msvc
-python3 "$X_PY" test --stage 2 src/tools/miri --target aarch64-apple-darwin
+case $HOST_TARGET in
+  x86_64-unknown-linux-gnu)
+    # Only this branch runs in PR CI.
+    # Fully test all main OSes, including a 32bit target.
+    python3 "$X_PY" test --stage 2 src/tools/miri --target x86_64-apple-darwin
+    python3 "$X_PY" test --stage 2 src/tools/miri --target i686-pc-windows-msvc
+    # Only run "pass" tests for the remaining targets, which is quite a bit faster.
+    python3 "$X_PY" test --stage 2 src/tools/miri --target x86_64-pc-windows-gnu --test-args pass
+    python3 "$X_PY" test --stage 2 src/tools/miri --target i686-unknown-linux-gnu --test-args pass
+    python3 "$X_PY" test --stage 2 src/tools/miri --target aarch64-unknown-linux-gnu --test-args pass
+    python3 "$X_PY" test --stage 2 src/tools/miri --target s390x-unknown-linux-gnu --test-args pass
+    ;;
+  x86_64-pc-windows-msvc)
+    # Strangely, Linux targets do not work here. cargo always says
+    # "error: cannot produce cdylib for ... as the target ... does not support these crate types".
+    # Only run "pass" tests, which is quite a bit faster.
+    python3 "$X_PY" test --stage 2 src/tools/miri --target aarch64-apple-darwin --test-args pass
+    python3 "$X_PY" test --stage 2 src/tools/miri --target i686-pc-windows-gnu --test-args pass
+    ;;
+  *)
+    echo "FATAL: unexpected host $HOST_TARGET"
+    exit 1
+    ;;
+esac
 unset BOOTSTRAP_SKIP_TARGET_SANITY
diff --git a/src/ci/github-actions/ci.yml b/src/ci/github-actions/ci.yml
index bbba6600581ea..2feb51920dff0 100644
--- a/src/ci/github-actions/ci.yml
+++ b/src/ci/github-actions/ci.yml
@@ -582,6 +582,7 @@ jobs:
           - name: x86_64-msvc-ext
             env:
               SCRIPT: python x.py --stage 2 test src/tools/cargotest src/tools/cargo && src/ci/docker/host-x86_64/x86_64-gnu-tools/checktools.sh x.py /tmp/toolstate/toolstates.json windows
+              HOST_TARGET: x86_64-pc-windows-msvc
               RUST_CONFIGURE_ARGS: --build=x86_64-pc-windows-msvc --enable-lld --save-toolstates=/tmp/toolstate/toolstates.json
               DEPLOY_TOOLSTATES_JSON: toolstates-windows.json
             <<: *job-windows-8c