Discrete topological problems are often relaxed with continuous design variables so that they can be solved using continuous mathematical programming. Such practice prevails because large-scale discrete 0-1 mathematical programming is not generally available. Although the relaxed problems become tractable, they may cause the appearance of intermediate density in the optimum topologies, especially those of structures and compliant mechanisms. Various penalty schemes have been proposed to suppress the intermediate density. Most of the past works assumed that the same penalty schemes could be effectively applied to both problems of stiffest structure design and compliant mechanism design. Differences in nature between the problems are generally neglected. This work distinguished the two problems, and observed that compliant mechanism (CM) problem does not suffer intermediate density as seriously as minimum compliance (MC) problem does. Besides allocating more material, explicit and implicit penalties were pursued to suppress intermediate density. To ensure mesh-independence and not to complicate the nonconvex objective function in CM problem, a new technique using a constraint of explicit penalty with variable bound is proposed to suppress intermediate density in topology optimization of compliant mechanisms. Together with a perimeter constraint, the new technique is also applied to MC problem.