Intelligent local management of data stream throttling in data movement operations, such as secondary-copy operations in a storage management system, is disclosed. A local throttling manager may intelligently interoperate with co-resident data agents and/or a media agent executing on any given local computing device, whether a client computing device or a secondary storage computing device. The local throttling manager may allocate and manage the available bandwidth for various jobs and their constituent data streams—across the data agents and/or media agent. Bandwidth is dynamically allocated and re-allocated to data streams used by ongoing jobs, in response to new jobs starting and old jobs completing, without having to pause and restart ongoing jobs to accommodate bandwidth adjustments. The illustrative embodiment also provides local users with a measure of control over data streams—to suspend, pause, and/or resume them—independently from the centralized storage manager that manages the storage management system as a whole.