Help Desk outsourcing works best as a way to improve organizations that are already efficient. If your operation runs poorly, outsourcing can actually increase cost and complexity while worsening the customer experience.
Before looking for vendors, do a reality check that involves careful assessment of your volumes, processes, and documentation. Be clear on your goals. Can your support really be improved by someone else at lower costs? If you choose to begin the process, prepare yourself for a slow and careful due diligence process. With well-established vendors, these contracts tend to involve long term commitments.
If a costly or ineffective support operation is driving you to consider outsourcing, take a deeper look in the corporate mirror before shopping for vendors. Outsourcing may actually force you to address those sticky internal issues anyway.