The performance of a UHF-band passive RFID system in a dense multi-reader environment is limited by both the reader-to-reader interference and reader-to-tag interference. In this paper, first, we propose a combination of subcarrier modulation backscattering and reduced carrier frequency offset among readers to reduce both the reader-to-reader interference and the reader-to-tag interference. Then, we propose a new distributed modulation index control scheme using the readers' estimation of the tag's SINR in order to further reduce the reader-to-tag interference. By adaptively controlling each reader's transmission modulation index, the asymmetric reader-to-tag interference can be effectively controlled to satisfy the required SINR of tags. Computer simulations show that the proposed scheme can reduce the minimum required inter-reader distance or increase the number of concurrently operable readers in dense multi-reader environments, especially when there are large differences in the levels of reader-to-tag interference. We show some optimizations of the proposed scheme for practical RFID applications. We also propose a bandwidth efficient modulation scheme for reader transmission which is suitable for the proposed modulation index control scheme.