A new hybrid BIST scheme is proposed which is based on using an "incrementally guided LFSR." It very efficiently combines external deterministic data from the tester with on-chip pseudo-random BIST. The hardware overhead is very small as a conventional STUMPS architecture [1] is used with only a small modification to the feedback of the LFSR which allows the tester to incrementally guide the LFSR so that it can embed patterns that detect the random-pattern-resistant faults in the pseudo-random sequence. Compared with external testing, the proposed approach achieves dramatic reductions in tester storage requirements while using very simple on-chip hardware. Results indicate that the proposed approach provides very attractive tradeoffs between test length and tester storage requirements.