diff --git a/common/config/rush/common-versions.json b/common/config/rush/common-versions.json
index bc7873115603..9a1670658b75 100644
--- a/common/config/rush/common-versions.json
+++ b/common/config/rush/common-versions.json
@@ -51,6 +51,10 @@
     // ]
     // Following is required to allow for backward compatibility with Event Processor Host Track 1
     "@azure/event-hubs": ["^2.1.4"],
+
+    // Exception for storage before the preview release
+    "@azure/core-http": ["^1.1.1"],
+
     // Allow packages to continue to use old eslint-plugin-azure-sdk until they can adapt to 3.0.0
     "@azure/eslint-plugin-azure-sdk": ["^2.0.1"]
   }
diff --git a/sdk/storage/storage-blob/package.json b/sdk/storage/storage-blob/package.json
index 2a0d7bec7031..2292e95e86a0 100644
--- a/sdk/storage/storage-blob/package.json
+++ b/sdk/storage/storage-blob/package.json
@@ -99,7 +99,7 @@
   },
   "dependencies": {
     "@azure/abort-controller": "^1.0.0",
-    "@azure/core-http": "^1.1.4",
+    "@azure/core-http": "^1.1.1",
     "@azure/core-lro": "^1.0.2",
     "@azure/core-paging": "^1.1.1",
     "@azure/core-tracing": "1.0.0-preview.8",
diff --git a/sdk/storage/storage-file-datalake/package.json b/sdk/storage/storage-file-datalake/package.json
index 7842c5f7f96d..56d848547ea8 100644
--- a/sdk/storage/storage-file-datalake/package.json
+++ b/sdk/storage/storage-file-datalake/package.json
@@ -95,7 +95,7 @@
   },
   "dependencies": {
     "@azure/abort-controller": "^1.0.0",
-    "@azure/core-http": "^1.1.4",
+    "@azure/core-http": "^1.1.1",
     "@azure/core-paging": "^1.1.1",
     "@azure/core-tracing": "1.0.0-preview.8",
     "@azure/logger": "^1.0.0",
diff --git a/sdk/storage/storage-file-share/package.json b/sdk/storage/storage-file-share/package.json
index 1885b3412d66..b31cb53ff00c 100644
--- a/sdk/storage/storage-file-share/package.json
+++ b/sdk/storage/storage-file-share/package.json
@@ -102,7 +102,7 @@
   },
   "dependencies": {
     "@azure/abort-controller": "^1.0.0",
-    "@azure/core-http": "^1.1.4",
+    "@azure/core-http": "^1.1.1",
     "@azure/core-paging": "^1.1.1",
     "@azure/core-tracing": "1.0.0-preview.8",
     "@azure/logger": "^1.0.0",
diff --git a/sdk/storage/storage-queue/package.json b/sdk/storage/storage-queue/package.json
index 65353d864097..6df69c18b6d9 100644
--- a/sdk/storage/storage-queue/package.json
+++ b/sdk/storage/storage-queue/package.json
@@ -99,7 +99,7 @@
   },
   "dependencies": {
     "@azure/abort-controller": "^1.0.0",
-    "@azure/core-http": "^1.1.4",
+    "@azure/core-http": "^1.1.1",
     "@azure/core-paging": "^1.1.1",
     "@azure/core-tracing": "1.0.0-preview.8",
     "@azure/logger": "^1.0.0",