We investigate several versions of restraineddomination numbers and present new bounds on these parameters. We generalize theconcept of restrained domination and improve some well-known bounds in the literature.In particular, for a graph G of order n and minimum degree δ≥3, we prove thatthe restrained double domination number of G is at most n−δ+1. In addition,for a connected cubic graph G of order n we show thatthe total restrained domination number of G is at least n/3 andthe restrained double domination number of G is at least n/2