Quality improvements in laser cutting of mild steel have been achieved by a newly developed model-based optimization strategy and its application to one-dimensional cut has been reported early. The specific aims of this paper are to assure quality of cut when cornering and generating small diameter holes. Such routines encompass a large proportion of all features processed on laser cutting systems, and therefore their successful production is significant. Currently, extensive trial-and-error based experimentation is needed in order to improve quality for these routines. Thus model-based optimization has the benefit of reducing this time-exhaustive step whilst leading to an optimal solution. Nonlinear power adaptation profiles are generated via the optimization strategy in order to stabilize cutting front temperatures. Uniform temperatures produce better quality by reducing (i) kerf widening effects, (ii) heat-affected zone extents, and (iii) workpiece self-burning effects. Experimental results are presented, and it is demonstrated that such process manipulation can produce significant quality improvements. In addition, predicted heat-affected zones correlate closely to those actually obtained. The process manipulation is successfully implemented in an industrial laser cutting system under laboratory condition.