Competition plays a crucial role in determining adaptation of species, yet we know little as to how adaptation is affected by the strength of competition. On the one hand, strong competition typically results in population size reductions, which can hamper adaptation due to a shortage of beneficial mutations; on the other hand, specificity of adaptation to competitors may offset the negative evolutionary consequences of such population size effects. Here, we investigate how competition strength affects population fitness in the bacterium Pseudomonas fluorescens. Our results demonstrate that strong competition constrains adaptation of focal populations, which can be partially explained by population size reductions. However, fitness assays also reveal specific adaptation of focal populations to particular competitors varying in competitive ability. Additionally, this specific adaptation can offset the negative effects of competitor-mediated population size reductions under strong competition. Our study therefore highlights the importance of opposing effects of strong competition on species adaptation, which may lead to different outcomes of colonization under intense and relaxed competitive environments in the context of population dispersal.