What models -- BSIMSOI?

I don't expect trapezoidal is helping your DC convergence (unless it's pseudo-tran); I guess I'd be surprised if changing the tolerances makes DC work better, either -- once you're close, Newton's method should work quite well to reduce the error, unless there's some error in the derivatives of the model (and if you're far away so Newton isn't quadratically converging, then increasing tolerances isn't likely to help).