The diffusive regime of double-diffusive convection generates staircases consisting of thin high-gradient interfaces sandwiched between convectively mixed layers. Simultaneous microstructure measurements of both temperature and conductivity from the staircases in Lake Kivu are used to test flux laws and theoretical models for double diffusion. Density ratios in Lake Kivu are between one and ten and mixed layer thicknesses on average 0.7 m. The larger interface thickness of temperature (average 9 cm) compared to dissolved substances (6 cm) confirms the boundary-layer structure of the interface. Our observations suggest that the boundary-layer break-off cannot be characterized by a single critical boundary-layer Rayleigh number, but occurs within a range of O(10(2)) to O(10(4)). Heat flux parameterizations which assume that the Nusselt number follows a power law increase with the Rayleigh number Ra are tested for their exponent . In contrast to the standard estimate =1/3, we found =0.200.03 for density ratios between two and six. Therefore, we suggest a correction of heat flux estimates which are based on =1/3. The magnitude of the correction depends on Ra in the system of interest. For Lake Kivu (average heat flux 0.10 W m(-2)) with Ra=O(10(8)), corrections are marginal. In the Arctic Ocean with Ra=O(10(8)) to O(10(12)), however, heat fluxes can be overestimated by a factor of four.