The development of texture in thin Cu and dilute binary Cu(Ti) and Cu(In) films has been investigated as a function of annealing history. The textures are comprised of <111>, <100> and <110> fiber in different proportions for the three films. Annealing strengthens the texture for all films. For the annealed films, alloying with Ti strengthens the <111> component, whereas alloying with In weakens it compared to pure copper. Two different approaches were used to derive volume fractions of texture components, namely fiber plots and orientation distributions. For strong mono-textured films of materials such as aluminum, fiber plots are most effective. For weaker, poly-textured films such as the copper alloys studied here, orientation distributions derived from pole figures provide the most reliable basis for quantitative characterization.