By (1, +k(n))-branching programs (b.p.'s) we mean those b.p.'s which during each of their computations are allowed to test at most k(n) input bits repeatedly. For a Boolean function computable within polynomial time a trade-off is presented between the size and the number of repeatedly tested input bits of any b.p. P computing the function. Namely, if at most k(n) repeated tests are allowed, where log 2 n k(n) n/(1000 log 2 n), then the size ofP is at least exp(Ω(n/(k(n)log 2 n)) 1 2 ). This is exponential wheneverk (n) n α for a fixed α < 1 and superpolynomial whenever k(n) = o(n/log 3 2 n).The presented result is a step towards a superpolynomial lower bound for 2-b.p.'s which is an open problem since 1984 when the first superpolynomial lower bounds for 1-b.p.'s were proven (Wegener, 1988; Zak, 1984). The present result is an improvement on (Zak, 1995).