The polar atmospheric boundary layer is often very shallow over sea-ice-covered regions so that the parametrization of the near-surface turbulent fluxes and thus of drag coefficients is particularly important for the exchange of energy and momentum between air and sea ice. In most climate and weather prediction models, the neutral drag coefficient is set constant. Observations show, however, a large variability of drag coefficients dependent on the sea ice morphology. The latter is characterized by parameters like concentration of sea ice, leads, and melt ponds as well as by their characteristic diameters, sea ice freeboard, ridge height and ridge distribution. A hierarchy of parametrizations of the neutral 10-m drag coefficients over polar sea ice is presented which account for different sea ice morphology regimes. The basic concept applies a partitioning of the total drag into skin drag and form drag. In the most simple version of the parametrization, the only sea ice parameter required is the sea ice concentration. It is shown by comparison with data that a part of the drag variability can be well explained by this most simple scheme. It is applicable to ice regimes with broken floes whose characteristic diameters are below 1 km so that form drag by floe edges contributes to the surface drag. The simple scheme can also be used in the inner Arctic regions during summer when melt ponds and leads dominate the ice regime. It is shown that some parametrizations of drag coefficients suggested earlier can be obtained as special cases within the new concept when specific simplifications concerning the floe and melt pond geometry are applied. The new derivation needs fewer assumptions than previous similar approaches. The final parametrizations can be applied to climate, weather prediction, and sea ice models for present sea ice conditions but also for future climate scenarios with changing parameter values.