diff --git a/bigquery/setup.py b/bigquery/setup.py
index 47ab9f560461..aa5a804a0d3b 100644
--- a/bigquery/setup.py
+++ b/bigquery/setup.py
@@ -30,7 +30,7 @@
 release_status = 'Development Status :: 4 - Beta'
 dependencies = [
     'google-cloud-core<0.29dev,>=0.28.0',
-    'google-api-core<2.0.0dev,>=0.1.5.dev1',
+    'google-api-core<2.0.0dev,>=1.0.0',
     'google-resumable-media>=0.2.1',
 ]
 extras = {
diff --git a/datastore/setup.py b/datastore/setup.py
index 3df20defb90a..667814e2851c 100644
--- a/datastore/setup.py
+++ b/datastore/setup.py
@@ -30,7 +30,7 @@
 release_status = 'Development Status :: 5 - Production/Stable'
 dependencies = [
     'google-cloud-core<0.29dev,>=0.28.0',
-    'google-api-core[grpc]<2.0.0dev,>=0.1.5.dev1',
+    'google-api-core[grpc]<2.0.0dev,>=1.0.0',
 ]
 extras = {
 }
diff --git a/logging/setup.py b/logging/setup.py
index a1b2fed2af05..5cb0e3c40a41 100644
--- a/logging/setup.py
+++ b/logging/setup.py
@@ -30,7 +30,7 @@
 release_status = 'Development Status :: 5 - Production/Stable'
 dependencies = [
     'google-cloud-core<0.29dev,>=0.28.0',
-    'google-api-core[grpc]<2.0.0dev,>=0.1.1',
+    'google-api-core[grpc]<2.0.0dev,>=1.0.0',
 ]
 extras = {
 }
diff --git a/spanner/setup.py b/spanner/setup.py
index c02f4c067a30..704e9fdb9845 100644
--- a/spanner/setup.py
+++ b/spanner/setup.py
@@ -30,7 +30,7 @@
 release_status = 'Development Status :: 4 - Beta'
 dependencies = [
     'google-cloud-core<0.29dev,>=0.28.0',
-    'google-api-core[grpc]<2.0.0dev,>=0.1.5.dev1',
+    'google-api-core[grpc]<2.0.0dev,>=1.0.0',
     'grpc-google-iam-v1<0.12dev,>=0.11.4',
 ]
 extras = {
diff --git a/trace/setup.py b/trace/setup.py
index 4b70c59f4ffa..e44831fe5190 100644
--- a/trace/setup.py
+++ b/trace/setup.py
@@ -30,7 +30,7 @@
 release_status = 'Development Status :: 3 - Alpha'
 dependencies = [
     'google-cloud-core<0.29dev,>=0.28.0',
-    'google-api-core[grpc]<2.0.0dev,>=0.1.1',
+    'google-api-core[grpc]<2.0.0dev,>=1.0.0',
 ]
 extras = {
 }