Evaporation of surfactant-laden sessile droplets is omnipresent in nature and industrial applications such as inkjet printing. Soluble surfactants start to form micelles in an aqueous solution for surfactant concentrations exceeding the critical micelle concentration (CMC). Here, the evaporation of aqueous sodium dodecyl sulfate (SDS) sessile droplets on hydrophobic surfaces was experimentally investigated for SDS concentrations ranging from 0.025 to 1 CMC. In contrast to the constant contact angle of an evaporating sessile water droplet, we observed that, at the same surface, the contact angle of an SDS laden droplet with concentration below 0.5 CMC first decreases, then increases, and finally decreases, resulting in a local contact angle minimum. Surprisingly, the minimum contact angle was found to be substantially lower than the static receding contact angle and decreased with decreasing initial SDS concentration. Furthermore, the bulk SDS concentration at the local contact angle minimum was found to decrease with decrease in the initial SDS concentration. The location of the observed contact angle minimum relative to the normalized evaporation time and its minimum value proved to be independent of both the relative humidity and droplet volume and thus of the total evaporation time. We discuss the observed contact angle dynamics in terms of the formation of a disordered layer of SDS molecules on the substrate at concentrations below 0.5 CMC. The present work underlines the complexity of the evaporation of sessile liquid-surfactant droplets and the influence of surfactant-substrate interactions on the evaporation process.