diff --git a/lib/git.js b/lib/git.js
index 000ee9fc..a2a6cbb7 100644
--- a/lib/git.js
+++ b/lib/git.js
@@ -254,8 +254,11 @@ class GitFetcher extends Fetcher {
           resolved: this.resolved,
           integrity: null, // it'll always be different, if we have one
         }).extract(tmp).then(() => handler(`${tmp}${this.spec.gitSubdir || ''}`), er => {
-          // fall back to ssh download if tarball fails
-          if (er.constructor.name.match(/^Http/)) {
+          // fall back to clone if the tarball download fails due to an
+          // HTTP error or if the response is not a valid tarball (e.g.
+          // a hosted provider returning an HTML sign-in page with 200)
+          if ((typeof er.statusCode === 'number' && er.statusCode >= 400) ||
+              /^TAR_/.test(er.code)) {
             return this.#clone(handler, false)
           } else {
             throw er
