diff --git a/sdk/storage/azure-storage-blobs/CHANGELOG.md b/sdk/storage/azure-storage-blobs/CHANGELOG.md
index 770d63294..f1cbd8558 100644
--- a/sdk/storage/azure-storage-blobs/CHANGELOG.md
+++ b/sdk/storage/azure-storage-blobs/CHANGELOG.md
@@ -12,6 +12,8 @@
 
 ### Other Changes
 
+- Create less threads if there isn't too much data to transfer.
+
 ## 12.1.0 (2021-08-10)
 
 ### Features Added
diff --git a/sdk/storage/azure-storage-common/inc/azure/storage/common/internal/concurrent_transfer.hpp b/sdk/storage/azure-storage-common/inc/azure/storage/common/internal/concurrent_transfer.hpp
index 602716b36..a67b4b34b 100644
--- a/sdk/storage/azure-storage-common/inc/azure/storage/common/internal/concurrent_transfer.hpp
+++ b/sdk/storage/azure-storage-common/inc/azure/storage/common/internal/concurrent_transfer.hpp
@@ -54,7 +54,7 @@ namespace Azure { namespace Storage { namespace _internal {
     };
 
     std::vector<std::future<void>> threadHandles;
-    for (int i = 0; i < concurrency - 1; ++i)
+    for (int i = 0; i < std::min<int64_t>(concurrency, numChunks) - 1; ++i)
     {
       threadHandles.emplace_back(std::async(std::launch::async, threadFunc));
     }
diff --git a/sdk/storage/azure-storage-files-datalake/CHANGELOG.md b/sdk/storage/azure-storage-files-datalake/CHANGELOG.md
index f4238d5c4..ca64f964a 100644
--- a/sdk/storage/azure-storage-files-datalake/CHANGELOG.md
+++ b/sdk/storage/azure-storage-files-datalake/CHANGELOG.md
@@ -12,6 +12,8 @@
 
 ### Other Changes
 
+- Create less threads if there isn't too much data to transfer.
+
 ## 12.1.0 (2021-08-10)
 
 ### Features Added
diff --git a/sdk/storage/azure-storage-files-shares/CHANGELOG.md b/sdk/storage/azure-storage-files-shares/CHANGELOG.md
index 32d7fe44e..e5795809b 100644
--- a/sdk/storage/azure-storage-files-shares/CHANGELOG.md
+++ b/sdk/storage/azure-storage-files-shares/CHANGELOG.md
@@ -12,6 +12,8 @@
 
 ### Other Changes
 
+- Create less threads if there isn't too much data to transfer.
+
 ## 12.1.0 (2021-08-10)
 
 ### Bugs Fixed