Twisted-ring-counters (TRCs) have been used as built-in test pattern generators for high-performance circuits due to their small area overhead, low performance impact and simple control circuitry. However, previous work based on a single, fixed-order TRC often requires long test time to achieve high fault coverage and large storage space to store required control data and TRC seeds. In this paper, a novel programmable multiple-TRC-based on-chip test generation scheme is proposed to minimize both the required test time and test data volume. The scan path of a circuit under test is divided into multiple equal-length scan segments, each converted to a small-size TRC controlled by a programmable control logic unit. An efficient algorithm to determine the required seeds and the control vectors is developed. Experimental results on ISCAS'89, ITC'99 and IWLS'05 benchmark circuits show that, on average, the proposed scheme using only a single programmable TRC design can achieve 35.58%-98.73% reductions on the number of test application cycles with smaller storage data volume compared with previous work. When using more programmable TRC designs, 83.60%-99.59% reductions can be achieved with only slight increase on test data volume.