diff --git a/client.go b/client.go
index 577e988a..aa17a392 100644
--- a/client.go
+++ b/client.go
@@ -1539,8 +1539,13 @@ func (f *File) WriteAt(b []byte, off int64) (written int, err error) {
 	return len(b), nil
 }
 
-// readFromConcurrent implements ReaderFrom, but works concurrently rather than sequentially.
-func (f *File) readFromConcurrent(r io.Reader, remain int64) (read int64, err error) {
+// ReadFromWithConcurrency implements ReaderFrom,
+// but uses the given concurrency to issue multiple requests at the same time.
+//
+// Giving a concurrency of less than one will default to the Client’s max concurrency.
+//
+// Otherwise, the given concurrency will be capped by the Client's max concurrency.
+func (f *File) ReadFromWithConcurrency(r io.Reader, concurrency int) (read int64, err error) {
 	// Split the write into multiple maxPacket sized concurrent writes.
 	// This allows writes with a suitably large reader
 	// to transfer data at a much faster rate due to overlapping round trip times.
@@ -1560,12 +1565,9 @@ func (f *File) readFromConcurrent(r io.Reader, remain int64) (read int64, err er
 	}
 	errCh := make(chan rwErr)
 
-	concurrency64 := remain/int64(f.c.maxPacket) + 1 // a bad guess, but better than no guess
-	if concurrency64 > int64(f.c.maxConcurrentRequests) || concurrency64 < 1 {
-		concurrency64 = int64(f.c.maxConcurrentRequests)
+	if concurrency > f.c.maxConcurrentRequests || concurrency < 1 {
+		concurrency = f.c.maxConcurrentRequests
 	}
-	// Now that concurrency64 is saturated to an int value, we know this assignment cannot possibly overflow.
-	concurrency := int(concurrency64)
 
 	pool := newBufPool(concurrency, f.c.maxPacket)
 
@@ -1694,12 +1696,23 @@ func (f *File) ReadFrom(r io.Reader) (int64, error) {
 		}
 
 		if remain < 0 {
-			remain = math.MaxInt64
+			// We can strongly assert that we want default max concurrency here.
+			return f.ReadFromWithConcurrency(r, f.c.maxConcurrentRequests)
 		}
 
 		if remain > int64(f.c.maxPacket) {
-			// Only use concurrency, if it would be at least two read/writes.
-			return f.readFromConcurrent(r, remain)
+			// Otherwise, only use concurrency, if it would be at least two packets.
+
+			// This is the best reasonable guess we can make.
+			concurrency64 := remain/int64(f.c.maxPacket) + 1
+
+			// We need to cap this value to an `int` size value to avoid overflow on 32-bit machines.
+			// So, we may as well pre-cap it to `f.c.maxConcurrentRequests`.
+			if concurrency64 > int64(f.c.maxConcurrentRequests) {
+				concurrency64 = int64(f.c.maxConcurrentRequests)
+			}
+
+			return f.ReadFromWithConcurrency(r, int(concurrency64))
 		}
 	}