diff --git a/src/uu/rm/src/rm.rs b/src/uu/rm/src/rm.rs
index 43a4f4780..ba764034a 100644
--- a/src/uu/rm/src/rm.rs
+++ b/src/uu/rm/src/rm.rs
@@ -255,7 +255,18 @@ fn handle_dir(path: &Path, options: &Options) -> bool {
             // correctly on Windows
             if let Err(e) = remove_dir_all(path) {
                 had_err = true;
-                show_error!("could not remove '{}': {}", path.display(), e);
+                if e.kind() == std::io::ErrorKind::PermissionDenied {
+                    // GNU compatibility (rm/fail-eacces.sh)
+                    // here, GNU doesn't use some kind of remove_dir_all
+                    // It will show directory+file
+                    show_error!(
+                        "cannot remove '{}': {}",
+                        path.display(),
+                        "Permission denied"
+                    );
+                } else {
+                    show_error!("cannot remove '{}': {}", path.display(), e);
+                }
             }
         } else {
             let mut dirs: VecDeque<DirEntry> = VecDeque::new();
@@ -314,7 +325,16 @@ fn remove_dir(path: &Path, options: &Options) -> bool {
                             }
                         }
                         Err(e) => {
-                            show_error!("cannot remove '{}': {}", path.display(), e);
+                            if e.kind() == std::io::ErrorKind::PermissionDenied {
+                                // GNU compatibility (rm/fail-eacces.sh)
+                                show_error!(
+                                    "cannot remove '{}': {}",
+                                    path.display(),
+                                    "Permission denied"
+                                );
+                            } else {
+                                show_error!("cannot remove '{}': {}", path.display(), e);
+                            }
                             return true;
                         }
                     }
@@ -352,7 +372,16 @@ fn remove_file(path: &Path, options: &Options) -> bool {
                 }
             }
             Err(e) => {
-                show_error!("removing '{}': {}", path.display(), e);
+                if e.kind() == std::io::ErrorKind::PermissionDenied {
+                    // GNU compatibility (rm/fail-eacces.sh)
+                    show_error!(
+                        "cannot remove '{}': {}",
+                        path.display(),
+                        "Permission denied"
+                    );
+                } else {
+                    show_error!("cannot remove '{}': {}", path.display(), e);
+                }
                 return true;
             }
         }
diff --git a/util/build-gnu.sh b/util/build-gnu.sh
index 64329bd0c..83136e733 100644
--- a/util/build-gnu.sh
+++ b/util/build-gnu.sh
@@ -44,7 +44,7 @@ sed -i 's|"\$@|/usr/bin/timeout 600 "\$@|' build-aux/test-driver
 # Change the PATH in the Makefile to test the uutils coreutils instead of the GNU coreutils
 sed -i "s/^[[:blank:]]*PATH=.*/  PATH='${BUILDDIR//\//\\/}\$(PATH_SEPARATOR)'\"\$\$PATH\" \\\/" Makefile
 sed -i 's| tr | /usr/bin/tr |' tests/init.sh
-make
+make -j "$(nproc)"
 # Generate the factor tests, so they can be fixed
 # Used to be 36. Reduced to 20 to decrease the log size
 for i in {00..20}
@@ -59,7 +59,7 @@ do
 done
 
 
-grep -rl 'path_prepend_' tests/* | xargs sed -i 's|path_prepend_ ./src||'
+grep -rl 'path_prepend_' tests/* | xargs sed -i 's| path_prepend_ ./src||'
 sed -i -e 's|^seq |/usr/bin/seq |' -e 's|sha1sum |/usr/bin/sha1sum |' tests/factor/t*sh
 
 # Remove tests checking for --version & --help
@@ -94,8 +94,26 @@ sed -i 's|cp |/usr/bin/cp |' tests/mv/hard-2.sh
 sed -i 's|paste |/usr/bin/paste |' tests/misc/od-endian.sh
 sed -i 's|seq |/usr/bin/seq |' tests/misc/sort-discrim.sh
 
-#Add specific timeout to tests that currently hang to limit time spent waiting
+# Add specific timeout to tests that currently hang to limit time spent waiting
 sed -i 's|seq \$|/usr/bin/timeout 0.1 seq \$|' tests/misc/seq-precision.sh tests/misc/seq-long-double.sh
 sed -i 's|cat |/usr/bin/timeout 0.1 cat |' tests/misc/cat-self.sh
 
+
+# Remove dup of /usr/bin/ when executed several times
+grep -rl '/usr/bin//usr/bin/' tests/* | xargs --no-run-if-empty sed -i 's|/usr/bin//usr/bin/|/usr/bin/|g'
+
+
+#### Adjust tests to make them work with Rust/coreutils
+# in some cases, what we are doing in rust/coreutils is good (or better)
+# we should not regress our project just to match what GNU is going.
+# So, do some changes on the fly
+
+sed -i -e "s|rm: cannot remove 'e/slink'|rm: cannot remove 'e'|g" tests/rm/fail-eacces.sh
+
+sed -i -e "s|rm: cannot remove 'a/b/file'|rm: cannot remove 'a'|g" tests/rm/cycle.sh
+
+sed -i -e "s|rm: cannot remove directory 'b/a/p'|rm: cannot remove 'b'|g" tests/rm/rm1.sh
+
+sed -i -e "s|rm: cannot remove 'a/1'|rm: cannot remove 'a'|g" tests/rm/rm2.sh
+
 test -f "${BUILDDIR}/getlimits" || cp src/getlimits "${BUILDDIR}"