This paper aims to establish conditions that guarantee the existence and uniqueness of a common fixed point for a pair of functions defined on a metric space, satisfying a type of contractive inequality involving distance-altering functions. We use some weaker forms of commuting maps to achieve our results, concretely, occasionally weakly compatible maps. We prove that if 𝑓,𝑔:(𝑋,𝑑)⟶(𝑋,𝑑)are occasionally weakly compatible maps with a coincident point such that𝜓(𝑑(𝑔(𝑥),𝑔(𝑦)))≤𝛼(𝑑(𝑓(𝑥),𝑓(𝑦)))∙𝜓(𝑑(𝑓(𝑥),𝑓(𝑦))),∀𝑥,𝑦∈𝑋where 𝛼:ℝ+⟶[0,1)and 𝜓is an altering distance function, then 𝑓and 𝑔have a unique common fixed point. This result generalizes some theorems of common fixed points where neither the continuity of maps nor the completeness of the metricspace is required.