diff --git a/cachito/workers/scm.py b/cachito/workers/scm.py
index 0df31ac2e..4c7013be1 100644
--- a/cachito/workers/scm.py
+++ b/cachito/workers/scm.py
@@ -158,9 +158,13 @@ def clone_and_archive(self, gitsubmodule=False):
                     self.url,
                     clone_path,
                     no_checkout=True,
+                    # Clone with depth 1 to save resources on large repos
+                    depth=1,
                     # Don't allow git to prompt for a username if we don't have access
                     env={"GIT_TERMINAL_PROMPT": "0"},
                 )
+
+                repo.remote().fetch(refspec=self.ref, depth=1)
             except:  # noqa E722
                 log.exception("Cloning the Git repository from %s failed", self.url)
                 raise CachitoError("Cloning the Git repository failed")
@@ -190,7 +194,7 @@ def update_and_archive(self, previous_archive, gitsubmodule=False):
             try:
                 # The reference must be specified to handle commits which are not part
                 # of a branch.
-                repo.remote().fetch(refspec=self.ref)
+                repo.remote().fetch(refspec=self.ref, depth=1)
             except:  # noqa E722
                 log.exception("Failed to fetch from remote %s", self.url)
                 raise CachitoError("Failed to fetch from the remote Git repository")