As manycores use dynamic energy ever more efficiently, static power consumption becomes a major concern. In particular, in a large manycore running at a low voltage, leakage in on-chip memory modules contributes substantially to the chip's power draw. This is unfortunate, given that, intuitively, the large multi-level cache hierarchy of a manycore is likely to contain a lot of useless data. An effective way to reduce this problem is to use a low-leakage technology such as embedded DRAM (eDRAM). However, eDRAM requires refresh. In this paper, we examine the opportunity of minimizing on-chip memory power further by intelligently refreshing on-chip eDRAM. We present Refrint, a simple approach to perform fine-grained, intelligent refresh of on-chip eDRAM multiprocessor cache hierarchies. We introduce the Refrint algorithms and microarchitecture. We evaluate Refrint in a simulated manycore running 16-threaded parallel applications. We show that an eDRAM-based memory hierarchy with Refrint consumes only 30% of the energy of a conventional SRAM-based memory hierarchy, and induces a slowdown of only 6%. In contrast, an eDRAM-based memory hierarchy without Refrint consumes 56% of the energy of the conventional memory hierarchy, inducing a slowdown of 25%.