diff --git a/README.md b/README.md
index 0bd698aa..751a149e 100644
--- a/README.md
+++ b/README.md
@@ -212,7 +212,8 @@ correct key is provided set in `git_crypt_key`.
   repository using the `--depth` option. To prevent newer commits that do
   not pass a `paths` filter test from skewing the cloned history away from
   `version.ref`, this resource will automatically deepen the clone until
-  `version.ref` is found again.
+  `version.ref` is found again. It will deepen with exponentially increasing steps
+  until a maximum of 127 + `depth` commits or else resort to unshallow the repository.
 
 * `fetch_tags`: *Optional.* If `true` the flag `--tags` will be used to fetch
   all tags in the repository. If `false` no tags will be fetched.
diff --git a/assets/deepen_shallow_clone_until_ref_is_found_then_check_out b/assets/deepen_shallow_clone_until_ref_is_found_then_check_out
index 881ff743..7f7a3733 100755
--- a/assets/deepen_shallow_clone_until_ref_is_found_then_check_out
+++ b/assets/deepen_shallow_clone_until_ref_is_found_then_check_out
@@ -3,12 +3,15 @@
 
 set -e
 
-readonly max_depth=128
+readonly max_depth=127
 
 declare depth="$1"
 readonly ref="$2"
 readonly tagflag="$3"
 
+declare total_depth="$depth"
+declare depth_from_ref=$((depth - 1))
+
 # A shallow clone may not contain the Git commit $ref:
 # 1. The depth of the shallow clone is measured backwards from the latest
 #    commit on the given head (master or branch), and in the meantime there may
@@ -24,7 +27,7 @@ readonly tagflag="$3"
 git_dir="$(git rev-parse --git-dir)"
 readonly git_dir
 
-while ! git checkout -q "$ref" &>/dev/null; do
+while ! git checkout -q "$ref~$depth_from_ref" &>/dev/null; do
   # once the depth of a shallow clone reaches the max depth of the origin
   # repo, Git silenty turns it into a deep clone
   if [ ! -e "$git_dir"/shallow ]; then
@@ -32,19 +35,20 @@ while ! git checkout -q "$ref" &>/dev/null; do
     break
   fi
 
-  echo "Could not find ref ${ref} in a shallow clone of depth ${depth}"
+  echo "Could not find ref ${ref}~${depth_from_ref} in a shallow clone of depth ${total_depth}"
 
   (( depth *= 2 ))
 
-  if [ "$depth" -gt "$max_depth" ]; then
+  if [ "$total_depth" -ge "$max_depth" ]; then
     echo "Reached depth threshold ${max_depth}, falling back to deep clone..."
     git fetch --unshallow origin $tagflag
 
     break
   fi
 
-  echo "Deepening the shallow clone to depth ${depth}..."
-  git fetch --depth "$depth" origin $tagflag
+  echo "Deepening the shallow clone by an additional ${depth}..."
+  git fetch --deepen "$depth" origin $tagflag
+  (( total_depth += depth ))
 done
 
 git checkout -q "$ref"
diff --git a/test/get.sh b/test/get.sh
index aeeb5272..e2b59af1 100755
--- a/test/get.sh
+++ b/test/get.sh
@@ -199,8 +199,8 @@ it_falls_back_to_deep_clone_if_ref_not_found() {
   local repo=$(init_repo)
   local ref1=$(make_commit $repo)
 
-  # 128 is the threshold when it starts doing a deep clone
-  for (( i = 0; i < 128; i++ )); do
+  # 127 is the threshold when it starts doing a deep clone
+  for (( i = 0; i < 127; i++ )); do
     make_commit $repo >/dev/null
   done
 
@@ -214,16 +214,56 @@ it_falls_back_to_deep_clone_if_ref_not_found() {
   test "$(git -C $dest rev-parse HEAD)" = $ref1
 
   echo "testing for msg 1" >&2
-  for d in 1 2 4 8 16 32 64 128; do
-    grep "Could not find ref ${ref1} in a shallow clone of depth ${d}" <$TMPDIR/stderr
+  for d in 1 3 7 15 31 63 127; do
+    grep "Could not find ref ${ref1}~0 in a shallow clone of depth ${d}" <$TMPDIR/stderr
   done
   echo "test for msg 1 done" >&2
 
-  for d in 2 4 8 16 32 64 128; do
-    grep "Deepening the shallow clone to depth ${d}..." <$TMPDIR/stderr
+  for d in 2 4 8 16 32 64; do
+    grep "Deepening the shallow clone by an additional ${d}..." <$TMPDIR/stderr
   done
 
-  grep "Reached depth threshold 128, falling back to deep clone..." <$TMPDIR/stderr
+  grep "Reached depth threshold 127, falling back to deep clone..." <$TMPDIR/stderr
+}
+
+it_considers_depth_if_ref_not_found() {
+  local repo=$(init_repo)
+  local depth=3
+
+  # make commits we're interested
+  local ref0=$(make_commit $repo)
+  local ref1=$(make_commit $repo)
+  local ref2=$(make_commit $repo)
+  local ref3=$(make_commit $repo)
+  
+  # make a total of 22 commits, so that ref0 is never fetched
+  for (( i = 0; i < 18; i++ )); do
+    make_commit $repo >/dev/null
+  done
+
+  local dest=$TMPDIR/destination
+
+  ( get_uri_at_depth_at_ref "file://$repo" $depth $ref3 $dest 3>&2- 2>&1- 1>&3- 3>&- | tee $TMPDIR/stderr ) 3>&1- 1>&2- 2>&3- 3>&- | jq -e "
+    .version == {ref: $(echo $ref3 | jq -R .)}
+  "
+
+  test -e $dest/some-file
+  test "$(git -C $dest rev-parse HEAD)" = $ref3
+  test "$(git -C $dest rev-parse HEAD~1)" = $ref2
+  test "$(git -C $dest rev-parse HEAD~2)" = $ref1
+  test -e "$dest/.git/shallow" # it's still shallow
+
+  echo "testing for 'could not find' messages'" >&2
+  for d in 3 9; do
+    grep "Could not find ref ${ref3}~2 in a shallow clone of depth ${d}" <$TMPDIR/stderr
+  done
+  echo "testing for 'could not find' messages done" >&2
+
+  echo "testing for 'deepening' messages'" >&2
+  for d in 6 12; do
+    grep "Deepening the shallow clone by an additional ${d}..." <$TMPDIR/stderr
+  done
+  echo "testing for 'deepening' messages' done" >&2
 }
 
 it_does_not_enter_an_infinite_loop_if_the_ref_cannot_be_found_and_depth_is_set() {
@@ -343,8 +383,8 @@ it_falls_back_to_deep_clone_of_submodule_if_ref_not_found() {
   local main_repo_last_commit_id=$(git -C $main_repo rev-parse HEAD)
   local submodule_repo_last_commit_id=$(git -C $submodule_repo rev-parse HEAD)
 
-  # 128 is the threshold when it starts doing a deep clone
-  for (( i = 0; i < 128; i++ )); do
+  # 127 is the threshold when it starts doing a deep clone
+  for (( i = 0; i < 127; i++ )); do
     make_commit $submodule_repo >/dev/null
   done
 
@@ -360,17 +400,21 @@ it_falls_back_to_deep_clone_of_submodule_if_ref_not_found() {
 
   test "$(git -C $main_repo rev-parse HEAD)" = $main_repo_last_commit_id
 
-  echo "testing for msg 1" >&2
-  for d in 1 2 4 8 16 32 64 128; do
-    grep "Could not find ref ${submodule_repo_last_commit_id} in a shallow clone of depth ${d}" <$TMPDIR/stderr
+  echo "testing for 'could not find' messages'" >&2
+  for d in 1 3 7 15 31 63 127; do
+    grep "Could not find ref ${submodule_repo_last_commit_id}~0 in a shallow clone of depth ${d}" <$TMPDIR/stderr
   done
-  echo "test for msg 1 done" >&2
+  echo "testing for 'could not find' messages done" >&2
 
-  for d in 2 4 8 16 32 64 128; do
-    grep "Deepening the shallow clone to depth ${d}..." <$TMPDIR/stderr
+  echo "testing for 'deepening' messages'" >&2
+  for d in 2 4 8 16 32 64; do
+    grep "Deepening the shallow clone by an additional ${d}..." <$TMPDIR/stderr
   done
+  echo "testing for 'deepening' messages' done" >&2
 
-  grep "Reached depth threshold 128, falling back to deep clone..." <$TMPDIR/stderr
+  echo "testing for 'reached threshold' message'" >&2
+  grep "Reached depth threshold 127, falling back to deep clone..." <$TMPDIR/stderr
+  echo "testing for 'reached threshold' message done'" >&2
 }
 
 it_fails_if_the_ref_cannot_be_found_while_deepening_a_submodule() {
@@ -767,6 +811,7 @@ run it_returns_list_of_tags_in_metadata
 run it_honors_the_depth_flag
 run it_can_get_from_url_at_depth_at_ref
 run it_falls_back_to_deep_clone_if_ref_not_found
+run it_considers_depth_if_ref_not_found
 run it_does_not_enter_an_infinite_loop_if_the_ref_cannot_be_found_and_depth_is_set
 run it_can_get_and_set_git_config
 run it_returns_same_ref