Please understand what the uncertainty principle means: like position measurements, momentum measurements yield precise answers--the "spread" here refers to the fact that measurements on identically prepared systems do not yield identical results. You can, if you want,construct a state such that repeated position measurements will be very close together, but you will pay a price: Momentum measurements on this state will be widely scattered. Or you can prepare a state with a reproducible momentum,but in that case, position measurements will be widely scattered. And,of course, if you're in a really bad mood you can create a state for which neither position nor momentum is well defined: