Consistency and optimality of block bootstrap schemes for distribution and variance estimation of smooth functionals of dependent data have been thoroughly investigated by Hall, Horowitz & Jing (1995), among others. However, for nonsmooth functionals, such as quantiles, much less is known. Existing results, due to Sun & Lahiri (2006), regarding strong consistency for distribution and variance estimation via the moving block bootstrap (MBB) require that b→∞, where b=⌊n/ℓ⌋ is the number of resampled blocks to be pasted together to form the bootstrap data series, n is the available sample size, and ℓ is the block length. Here we show that, in fact, weak consistency holds for any b such that 1≤b=O(n/ℓ). In other words we show that a hybrid between the subsampling bootstrap (b=1) and MBB is consistent. Empirical results illustrate the performance of hybrid block bootstrap estimators for varying numbers of blocks.