High power consumption will not only shorten the battery life of handheld devices, but also cause thermal and reliability problems. To lower power consumption, one way is to reduce the supply voltage as in multisupply voltage (MSV) designs. In region-based MSV, a circuit will be partitioned into "voltage islands" where each island occupies a contiguous physical space and operates at one supply voltage. In the work of Wu et al. [2005], this voltage supply problem is addressed, and the input placement is partitioned into a set of rectangular voltage islands by a slicing structure. However, the constraint of using a slicing structure prohibits better solutions in their approach. In the work of Ching et al. [2006], the constraint of obtaining rectangular shapes is relaxed; their method forms islands of very irregular shapes. In this article, we propose a method that focuses on forming rectangular voltage islands to minimize the power consumption, while at the same time favoring the power routing step. It is found that, even with this reduced flexibility on island shapes, we can still perform as well as, or in some cases, even better than the previous work of Ching et al. [2006] that does not control the shapes of the islands, in terms of power saving and island number.