The bit-wise unequal error protection problem, for the case when the number of groups of bits is fixed, is considered for variable-length block codes with feedback. An encoding scheme based on fixed-length block codes with erasures is used to establish inner bounds to the achievable performance for finite expected decoding time. A new technique for bounding the performance of variable-length block codes is used to establish outer bounds to the performance for a given expected decoding time. The inner and the outer bounds match one another asymptotically and characterize the achievable region of rate-exponent vectors, completely. The single-message message-wise unequal error protection problem for variable-length block codes with feedback is also solved as a necessary step on the way.