diff --git a/.github/workflows/staticcheck.yml b/.github/workflows/staticcheck.yml
index a1deb93b5..adf936d8a 100644
--- a/.github/workflows/staticcheck.yml
+++ b/.github/workflows/staticcheck.yml
@@ -21,6 +21,9 @@ jobs:
     - name: Check out code
       uses: actions/checkout@v3
 
+    - name: Run gofmt (goimports)
+      run: go run golang.org/x/tools/cmd/goimports -d --format-only .
+
     - name: Run go vet
       run: go vet ./...
 
diff --git a/internal/tooldeps/tooldeps.go b/internal/tooldeps/tooldeps.go
index babd897ae..92c25ff28 100644
--- a/internal/tooldeps/tooldeps.go
+++ b/internal/tooldeps/tooldeps.go
@@ -2,8 +2,12 @@
 // Use of this source code is governed by a BSD-style
 // license that can be found in the LICENSE file.
 
+//go:build for_go_mod_tidy_only
+// +build for_go_mod_tidy_only
+
 package tooldeps
 
 import (
 	_ "github.com/tailscale/depaware/depaware"
+	_ "golang.org/x/tools/cmd/goimports"
 )