diff --git a/modules/cloud-function-v1/README.md b/modules/cloud-function-v1/README.md
index cd8fbe86..ca432119 100644
--- a/modules/cloud-function-v1/README.md
+++ b/modules/cloud-function-v1/README.md
@@ -157,7 +157,7 @@ The Cloud Function bundle can be configured via the `bundle_config` variable, so
 
 If a `zip` archive is already available, simply set the archive path in `bundle_config.path`. If a dynamically generated archive is needed, set `bundle_config.path` to the source folder path, then optionally configure the path where the archive will be created, and any exclusions needed in the archive.
 
-In order to help prevent `archive_zip.output_md5` from changing cross platform (e.g. Cloud Build vs your local development environment), you'll have to make sure that the files included in the zip are always the same.
+If you use a folder and dynamic archive bundling, be mindful that the MD5 checksum of the generated `zip` file does not change across environments (e.g. Cloud Build vs your local development environment), by ensuring that the files in the folder are always the same.
 
 ```hcl
 module "cf-http" {
diff --git a/modules/cloud-function-v1/bundle.tf b/modules/cloud-function-v1/bundle.tf
index 2553d23a..8843672a 100644
--- a/modules/cloud-function-v1/bundle.tf
+++ b/modules/cloud-function-v1/bundle.tf
@@ -16,9 +16,9 @@
 
 locals {
   bundle = {
-    md5 = try(
-      data.archive_file.bundle[0].output_md5,
-      data.local_file.bundle[0].content_md5
+    name = try(
+      "bundle-${data.archive_file.bundle[0].output_md5}.zip",
+      basename(var.bundle_config.path)
     )
     path = try(
       data.archive_file.bundle[0].output_path,
@@ -57,7 +57,7 @@ resource "google_storage_bucket" "bucket" {
 }
 
 resource "google_storage_bucket_object" "bundle" {
-  name   = "bundle-${local.bundle.md5}.zip"
+  name   = local.bundle.name
   bucket = local.bucket
   source = local.bundle.path
 }
@@ -72,10 +72,3 @@ data "archive_file" "bundle" {
   output_file_mode = "0644"
   excludes         = var.bundle_config.excludes
 }
-
-data "local_file" "bundle" {
-  count = (
-    try(fileexists(var.bundle_config.path), null) == null ? 0 : 1
-  )
-  filename = var.bundle_config.path
-}
diff --git a/modules/cloud-function-v2/README.md b/modules/cloud-function-v2/README.md
index 78b05afc..f8bd9ead 100644
--- a/modules/cloud-function-v2/README.md
+++ b/modules/cloud-function-v2/README.md
@@ -171,7 +171,7 @@ The Cloud Function bundle can be configured via the `bundle_config` variable, so
 
 If a `zip` archive is already available, simply set the archive path in `bundle_config.path`. If a dynamically generated archive is needed, set `bundle_config.path` to the source folder path, then optionally configure the path where the archive will be created, and any exclusions needed in the archive.
 
-In order to help prevent `archive_zip.output_md5` from changing cross platform (e.g. Cloud Build vs your local development environment), you'll have to make sure that the files included in the zip are always the same.
+If you use a folder and dynamic archive bundling, be mindful that the MD5 checksum of the generated `zip` file does not change across environments (e.g. Cloud Build vs your local development environment), by ensuring that the files in the folder are always the same.
 
 ```hcl
 module "cf-http" {
diff --git a/modules/cloud-function-v2/bundle.tf b/modules/cloud-function-v2/bundle.tf
index 2553d23a..8843672a 100644
--- a/modules/cloud-function-v2/bundle.tf
+++ b/modules/cloud-function-v2/bundle.tf
@@ -16,9 +16,9 @@
 
 locals {
   bundle = {
-    md5 = try(
-      data.archive_file.bundle[0].output_md5,
-      data.local_file.bundle[0].content_md5
+    name = try(
+      "bundle-${data.archive_file.bundle[0].output_md5}.zip",
+      basename(var.bundle_config.path)
     )
     path = try(
       data.archive_file.bundle[0].output_path,
@@ -57,7 +57,7 @@ resource "google_storage_bucket" "bucket" {
 }
 
 resource "google_storage_bucket_object" "bundle" {
-  name   = "bundle-${local.bundle.md5}.zip"
+  name   = local.bundle.name
   bucket = local.bucket
   source = local.bundle.path
 }
@@ -72,10 +72,3 @@ data "archive_file" "bundle" {
   output_file_mode = "0644"
   excludes         = var.bundle_config.excludes
 }
-
-data "local_file" "bundle" {
-  count = (
-    try(fileexists(var.bundle_config.path), null) == null ? 0 : 1
-  )
-  filename = var.bundle_config.path
-}