We report on the structure of dendritic polyelectrolytes accompanied by counterions in a good, salt-free, implicit solvent using Langevin dynamics simulations and a Flory-type approach. Our focus is on the modification of charged dendrimer conformations via the strength of electrostatic interactions and the counterion excluded volume. We study the effects caused by charges by varying the reduced Bjerrum length, lambda(B)*, between the extremes of weak and strong electrostatic interactions. The counterion excluded volume was controlled by the size of ions. We investigate counterions ranging from conventional ones, with the size comparable to the monomer size, to bulky ions. Our results indicate that, as compared to neutral dendrimers, dendritic polyelectrolytes exist in swollen conformations, and the degree of swelling changes non-monotonically with increasing lambda(B)*. For weak electrostatic couplings, counterion density within dendrimers is minor and their radius of gyration subtly exceeds the size of neutral dendrimers. For intermediate electrostatic couplings, Coulomb attraction between opposite charges promotes absorption of ions into dendrimers' pervaded volume and counterion condensation on charged monomers. As a result, counterion density inside dendrimers abruptly increases and the ionic size starts to play a crucial role. In this regime, we observe that swelling of dendrimers reaches its maximum and is more pronounced for bulky counterions. For strong electrostatic couplings, complete condensation of conventional counterions proceeds, whereas for bulky ions condensation remains partial. In this regime, dendrimers deswell. In particular, in the presence of conventional ions, dendrimers collapse into globules, while, for bulky counterions, deswelling is suppressed.