diff --git a/test/apiv2/44-mounts.at b/test/apiv2/44-mounts.at
index 901245da68..d54669e7d0 100644
--- a/test/apiv2/44-mounts.at
+++ b/test/apiv2/44-mounts.at
@@ -6,7 +6,7 @@ podman pull $IMAGE &>/dev/null
 tmpfs_name="/mytmpfs"
 t POST containers/create?name=hostconfig_test \
   Image=$IMAGE \
-  Cmd='["df"]' \
+  Cmd='["df","-P","'$tmpfs_name'"]' \
   HostConfig='{"Binds":["/tmp/doesnotexist:/test1"]' \
   TmpFs="{\"$tmpfs_name\":\"rw\"}}" \
   201 \
@@ -22,5 +22,10 @@ t POST containers/${cid}/start 204
 t POST containers/${cid}/wait  200
 t GET  containers/${cid}/logs?stdout=true  200
 
-like "$(<$WORKDIR/curl.result.out)" ".* ${tmpfs_name}" \
+# /logs returns application/octet-stream, which our test helper saves in
+# an outfile rather than returning in $output. That's why we can't test
+# this directly in the /logs test above; instead, we rely on knowing the
+# path to the stored results. The 'tr' is needed because there may be
+# null bytes in the outfile.
+like "$(tr -d \\0 <$WORKDIR/curl.result.out)" ".* ${tmpfs_name}" \
      "'df' output includes tmpfs name"
diff --git a/test/system/065-cp.bats b/test/system/065-cp.bats
index 73e807843c..679cdc2095 100644
--- a/test/system/065-cp.bats
+++ b/test/system/065-cp.bats
@@ -370,6 +370,7 @@ load helpers
     is "${lines[0]}" "${randomcontent[0]}" "eval symlink - created container"
     is "${lines[1]}" "${randomcontent[1]}" "eval symlink - created container"
     run_podman rm -f cpcontainer
+    run_podman rmi $cpimage
 }
 
 
diff --git a/test/system/070-build.bats b/test/system/070-build.bats
index d413b0c103..8f6cdb46b6 100644
--- a/test/system/070-build.bats
+++ b/test/system/070-build.bats
@@ -241,11 +241,21 @@ EOF
         build_arg_implicit+="=$arg_implicit_value"
     fi
 
+    # FIXME FIXME FIXME: 2021-03-15: workaround for #9567 (slow ubuntu 2004):
+    # we're seeing lots of timeouts in CI. Until/unless #9567 gets fixed,
+    # let's get CI passing by extending the timeout when remote on ubuntu
+    local localtimeout=${PODMAN_TIMEOUT}
+    if is_remote; then
+        if grep -qi ubuntu /etc/os-release; then
+            localtimeout=$(( 2 * $localtimeout ))
+        fi
+    fi
+
     # cd to the dir, so we test relative paths (important for podman-remote)
     cd $PODMAN_TMPDIR
     export arg_explicit="THIS SHOULD BE OVERRIDDEN BY COMMAND LINE!"
     export arg_implicit=${arg_implicit_value}
-    run_podman ${MOUNTS_CONF} build \
+    PODMAN_TIMEOUT=$localtimeout run_podman ${MOUNTS_CONF} build \
                --build-arg arg_explicit=${arg_explicit_value} \
                $build_arg_implicit \
                --dns-search $nosuchdomain \
@@ -594,34 +604,46 @@ EOF
     run_podman rmi -a --force
 }
 
+# Caveat lector: this test was mostly copy-pasted from buildah in #9275.
+# It's not entirely clear what it's testing, or if the 'mount' section is
+# necessary.
 @test "build with copy-from referencing the base image" {
-  skip_if_rootless "cannot mount as rootless"
-  target=busybox-derived
-  target_mt=busybox-mt-derived
+  target=derived
+  target_mt=derived-mt
   tmpdir=$PODMAN_TMPDIR/build-test
   mkdir -p $tmpdir
+
   containerfile1=$tmpdir/Containerfile1
-    cat >$containerfile1 <<EOF
-FROM quay.io/libpod/busybox AS build
-RUN rm -f /bin/paste
+  cat >$containerfile1 <<EOF
+FROM $IMAGE AS build
+RUN rm -f /etc/issue
 USER 1001
-COPY --from=quay.io/libpod/busybox /bin/paste /test/
+COPY --from=$IMAGE /etc/issue /test/
 EOF
+
   containerfile2=$tmpdir/Containerfile2
-    cat >$containerfile2 <<EOF
-FROM quay.io/libpod/busybox AS test
-RUN rm -f /bin/nl
+  cat >$containerfile2 <<EOF
+FROM $IMAGE AS test
+RUN rm -f /etc/alpine-release
 FROM quay.io/libpod/alpine AS final
-COPY --from=quay.io/libpod/busybox /bin/nl /test/
+COPY --from=$IMAGE /etc/alpine-release /test/
 EOF
-  run_podman build -t ${target} -f ${containerfile1} ${tmpdir}
-  run_podman build --jobs 4 -t ${target} -f ${containerfile1} ${tmpdir}
 
-  run_podman build -t ${target} -f ${containerfile2} ${tmpdir}
+  # Before the build, $IMAGE's base image should not be present
+  local base_image=quay.io/libpod/alpine:latest
+  run_podman 1 image exists $base_image
+
+  run_podman build --jobs 1 -t ${target} -f ${containerfile2} ${tmpdir}
   run_podman build --no-cache --jobs 4 -t ${target_mt} -f ${containerfile2} ${tmpdir}
 
+  # After the build, the base image should exist
+  run_podman image exists $base_image
+
   # (can only test locally; podman-remote has no image mount command)
-  if ! is_remote; then
+  # (can also only test as root; mounting under rootless podman is too hard)
+  # We perform the test as a conditional, not a 'skip', because there's
+  # value in testing the above 'build' commands even remote & rootless.
+  if ! is_remote && ! is_rootless; then
     run_podman image mount ${target}
     root_single_job=$output
 
@@ -629,8 +651,21 @@ EOF
     root_multi_job=$output
 
     # Check that both the version with --jobs 1 and --jobs=N have the same number of files
-    test $(find $root_single_job -type f | wc -l) = $(find $root_multi_job -type f | wc -l)
+    nfiles_single=$(find $root_single_job -type f | wc -l)
+    nfiles_multi=$(find $root_multi_job -type f | wc -l)
+    run_podman image umount ${target_mt}
+    run_podman image umount ${target}
+
+    is "$nfiles_single" "$nfiles_multi" \
+       "Number of files (--jobs=1) == (--jobs=4)"
+
+    # Make sure the number is reasonable
+    test "$nfiles_single" -gt 50
   fi
+
+  # Clean up
+  run_podman rmi ${target_mt} ${target} ${base_image}
+  run_podman image prune -f
 }
 
 @test "podman build --logfile test" {
diff --git a/test/system/120-load.bats b/test/system/120-load.bats
index 936449bdb2..95113c4a6d 100644
--- a/test/system/120-load.bats
+++ b/test/system/120-load.bats
@@ -31,6 +31,9 @@ verify_iid_and_name() {
     invalid=$PODMAN_TMPDIR/invalid
     echo "I am an invalid file and should cause a podman-load error" > $invalid
     run_podman 125 load -i $invalid
+    # podman and podman-remote emit different messages; this is a common string
+    is "$output" ".*error pulling image: unable to pull .*" \
+       "load -i INVALID fails with expected diagnostic"
 }
 
 @test "podman save to pipe and load" {
diff --git a/test/system/700-play.bats b/test/system/700-play.bats
index e7904f59f8..8fa96741c0 100644
--- a/test/system/700-play.bats
+++ b/test/system/700-play.bats
@@ -5,6 +5,20 @@
 
 load helpers
 
+# This is a long ugly way to clean up pods and remove the pause image
+function teardown() {
+    run_podman pod rm -f -a
+    run_podman rm -f -a
+    run_podman image list --format '{{.ID}} {{.Repository}}'
+    while read id name; do
+        if [[ "$name" =~ /pause ]]; then
+            run_podman rmi $id
+        fi
+    done <<<"$output"
+
+    basic_teardown
+}
+
 testYaml="
 apiVersion: v1
 kind: Pod
@@ -24,7 +38,7 @@ spec:
       value: xterm
     - name: container
       value: podman
-    image: quay.io/libpod/alpine:latest
+    image: $IMAGE
     name: test
     resources: {}
     securityContext: