Incentives for keeping contractor/GC motivated to keep bids low?

[Nick O.]

Contractor currently charges % on total spent which gives him no motivation to keep bids low or fight for better deals with subs/suppliers. Wanted to get some ideas on how I can incentivize him to be motivated to get the job done for as low as possible without obviously cutting corners. Was thinking maybe paying him a % of the total job plus a % of profits but I've hear pro's and cons about giving a % of profits. Another idea was offering a bonus for coming under budget but wanted to see what amount of money would make most sense. Any feedback would be greatly appreciated!