We show how the characteristics of the evolutionary algorithm influence the evolvability of candidate solutions, i.e. the propensity of evolving individuals to generate better solutions as a result of genetic variation. More specifically, (1+λ) evolutionary strategies largely outperform (μ+1) evolutionary strategies in the context of the evolution of digital circuits --- a domain characterized by a high level of neutrality. This difference is due to the fact that the competition for robustness to mutations among the circuits evolved with (μ+1) evolutionary strategies leads to the selection of phenotypically simple but low evolvable circuits. These circuits achieve robustness by minimizing the number of functional genes rather than by relying on redundancy or degeneracy to buffer the effects of mutations. The analysis of these factors enabled us to design a new evolutionary algorithm, named Parallel Stochastic Hill Climber (PSHC), which outperforms the other two methods considered.