diff --git a/CHANGELOG_PENDING.md b/CHANGELOG_PENDING.md
index 25ac3bf15..8f9296c07 100644
--- a/CHANGELOG_PENDING.md
+++ b/CHANGELOG_PENDING.md
@@ -22,4 +22,6 @@ Friendly reminder, we have a [bug bounty program](https://hackerone.com/tendermi
 
 ### IMPROVEMENTS
 
+- [statesync] \#5516 Check that all heights necessary to rebuild state for a snapshot exist before adding the snapshot to the pool. (@erikgrinaker)
+
 ### BUG FIXES
diff --git a/statesync/stateprovider.go b/statesync/stateprovider.go
index 1e21b0aaf..4b1c75e32 100644
--- a/statesync/stateprovider.go
+++ b/statesync/stateprovider.go
@@ -94,6 +94,22 @@ func (s *lightClientStateProvider) AppHash(ctx context.Context, height uint64) (
 	if err != nil {
 		return nil, err
 	}
+	// We also try to fetch the blocks at height H and H+2, since we need these
+	// when building the state while restoring the snapshot. This avoids the race
+	// condition where we try to restore a snapshot before H+2 exists.
+	//
+	// FIXME This is a hack, since we can't add new methods to the interface without
+	// breaking it. We should instead have a Has(ctx, height) method which checks
+	// that the state provider has access to the necessary data for the height.
+	// We piggyback on AppHash() since it's called when adding snapshots to the pool.
+	_, err = s.lc.VerifyLightBlockAtHeight(ctx, int64(height+2), time.Now())
+	if err != nil {
+		return nil, err
+	}
+	_, err = s.lc.VerifyLightBlockAtHeight(ctx, int64(height), time.Now())
+	if err != nil {
+		return nil, err
+	}
 	return header.AppHash, nil
 }