[en] The usual description of dust-modified ion-acoustic and dust-acoustic solitons in plasmas containing negative dust is in terms of Boltzmann distributions for the hotter species. In the dust-modified ion-acoustic regime, besides positive potential solitons, negative structures can also be generated, for electrons with a polytropic index gamma(e)not equal 1, as well as for Boltzmann electrons, subject to conditions that are not too stringent. These general conditions were previously either ignored or given for weakly nonlinear solutions only. In the dust-acoustic domain in plasmas with negatively charged dust, however, only negative potential solitons can occur, even when the lighter species have non-Boltzmann distributions. For Boltzmann electrons only an infinite dust compression limits the soliton amplitudes and corresponding Mach numbers, whereas for gamma(e)not equal 1, the electron density, too, can be a limiting factor for the existence domain of such solitons. (c) 2005 American Institute of Physics.