diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index e316dc7117..19882a70d7 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -9,8 +9,12 @@ jobs:
     - uses: actions/checkout@v3
 
     - name: Clone Flutter SDK
+      # We can't do a depth-1 clone, because we need the most recent tag
+      # so that Flutter knows its version and sees the constraint in our
+      # pubspec is satisfied.  It's uncommon for flutter/flutter to go
+      # more than 100 commits between tags.  Fetch 1000 for good measure.
       run: |
-        git clone https://github.com/flutter/flutter ~/flutter
+        git clone --depth=1000 https://github.com/flutter/flutter ~/flutter
         TZ=UTC git --git-dir ~/flutter/.git log -1 --format='%h | %ci | %s' --date=iso8601-local
         echo ~/flutter/bin >> "$GITHUB_PATH"