This work explores constraints self-similarity imposes on the growth of the convective boundary layer. Most existent boundary layer schemes fail to use this simple constraint when formulating their mixing rules, moreover many schemes choose mixing rules independent of how they diagnose the boundary layer depth. For a convective boundary layer growing self-similarly, all of these issues should be connected. In this work we first explore the nature of the self-similarity constraint in the convective boundary layer, and then we show how it can be used to constrain mixing rules in the interior of the boundary layer, and the manner in which such rules can be matched to the free atmosphere on the one hand, and the surface on the other. We also show that formulating things in this manner greatly reduces the sensitivity of the model to the formulation for estimating the boundary layer depth. Lastly we evaluate more commonly used mixing schemes from the perspective of the similarity constraint. In this respect special attention is focused on the K-profile method. It is shown that to maintain the level where the buoyancy profile is neutrally stratified at a reasonable height, similarity constrains the form of the interior mixing rules.