We propose improvements and extensions to an analytical model of magnetization reversal in ultrathin flat dots and stripes with in-plane uniaxial anisotropy. Owing to the localized character of nucleation volumes in hard magnetic materials, we use the concept of edge demagnetizing torque, where all demagnetizing effects are applied at the dot's edge. The magnetization state and the reversal field hr are predicted as a function of magnetization, dot thickness and in-plane edge orientation. An excellent agreement is found with numerical simulations. An approximate but accurate scaling law is proposed for an easy computation of hr: The model is shown to be valid for dots thinner than both exchange length and wall width, and lateral size well above each of these lengths.