diff --git a/google/cloud/storage/parallel_upload.cc b/google/cloud/storage/parallel_upload.cc
index 1a1e14723ab07..8d4e7d05cd41f 100644
--- a/google/cloud/storage/parallel_upload.cc
+++ b/google/cloud/storage/parallel_upload.cc
@@ -381,7 +381,8 @@ Status ParallelUploadFileShard::Upload() {
     left_to_upload_ = 0;
     return status;
   };
-  auto const already_uploaded = ostream_.next_expected_byte();
+  auto const already_uploaded =
+      static_cast<std::int64_t>(ostream_.next_expected_byte());
   if (already_uploaded > left_to_upload_) {
     return fail(StatusCode::kInternal, "Corrupted upload state, uploaded " +
                                            std::to_string(already_uploaded) +
@@ -395,17 +396,13 @@ Status ParallelUploadFileShard::Upload() {
     return fail(StatusCode::kNotFound, "cannot open upload file source");
   }
 
-  static_assert(sizeof(std::ifstream::off_type) >= sizeof(std::uintmax_t),
-                "files cannot handle uintmax_t for offsets uploads");
-
-  // TODO(#...) - this cast should not be necessary.
-  istream.seekg(static_cast<std::ifstream::off_type>(offset_in_file_));
+  istream.seekg(offset_in_file_);
   if (!istream.good()) {
     return fail(StatusCode::kInternal, "file changed size during upload?");
   }
   while (left_to_upload_ > 0) {
-    auto const to_copy = static_cast<std::ifstream::off_type>(
-        std::min<std::uintmax_t>(left_to_upload_, upload_buffer_size_));
+    auto const to_copy = static_cast<std::streamsize>(
+        std::min<std::int64_t>(left_to_upload_, upload_buffer_size_));
     istream.read(buf.data(), to_copy);
     if (!istream.good()) {
       return fail(StatusCode::kInternal, "cannot read from file source");
diff --git a/google/cloud/storage/parallel_upload.h b/google/cloud/storage/parallel_upload.h
index 9d2e0e6404490..9822be23365d9 100644
--- a/google/cloud/storage/parallel_upload.h
+++ b/google/cloud/storage/parallel_upload.h
@@ -365,8 +365,12 @@ class ParallelUploadFileShard {
   std::shared_ptr<ParallelUploadStateImpl> state_;
   ObjectWriteStream ostream_;
   std::string file_name_;
-  std::uintmax_t offset_in_file_;
-  std::uintmax_t left_to_upload_;
+  // GCS only supports objects up to 5TiB, that fits comfortably in a
+  // `std::int64_t`, allows for any expected growth on that limit (not that we
+  // anticipate any), and plays nicer with the types in the standard C++
+  // library.
+  std::int64_t offset_in_file_;
+  std::int64_t left_to_upload_;
   std::size_t upload_buffer_size_;
   std::string resumable_session_id_;
 };