My rough swag equates to about one company of combat arms or MPs, mixed in with reinforcing attachments of CA/PSYOP/SF elements, at around a rough total of 130-140 troops. Center them on key terrain in the city and control the streets and alleyways. Each of these elements should have a counterpart IP/IA element.

I don't have a map of Baghdad handy anymore, but does anyone care to crunch the numbers on how many companies it would require, at a ratio of one for every 4 sq kms?