Grain design takes the central place in a solid rocket motor design activity. Ballistic quality of a designed grain can be evaluated by two vital indexes known as neutrality and sliver content. Sliver content results in tail-off of the thrust-time curve. These two measures of merit are an important part of acceptable grain design. This paper is restricted to the study of convex port star grain geometry and describes parametric evaluation to assess the effects of seven independent and defining geometric variables of the star and other ballistic factors including density of propellant and characteristic exhaust velocity on the burn pattern and performance profile for qualitative analysis of sliver fraction (tail-off)and neutrality. The purpose of the study is to expand the design domain by evaluating entire convex Star family under both neutral and least sliver content conditions. The computer program associated to it is essentially the ballistic design analysis of the convex star grain configuration. Results showed that neutrality and sliver fraction are dependent on certain parameters. It has been observed that for good neutrality, higher angular fraction and star angle close to neutrality must be maintained. Sliver fraction depends upon the star geometry and can be reduced by decreasing angular fraction leading to reduced tail-off. Thus neutrality and reduced tail-off cannot be achieved simultaneously and trade-off has to be made. However, higher value of characteristic exhaust velocity (C*) will reduce tail-off.