Natal dispersal capture-recapture data from five fragmented populations of house sparrows, great tits, and blue tits were analyzed using maximum likelihood methods. A new two-parametric distribution was constructed that includes four distributions previously used as special cases in the literature. Dispersal standard deviations were estimated at 22.9 km for the house sparrows and ranged from 0.66 to 4.4 km for the tits. Female great tits and blue tits dispersed consistently further than males. Estimates of the shape parameter of the dispersal distribution ranged from 0.66 to 2.27, indicating strong to moderately leptokurtic dispersal displacements. There were significant effects of density on local immigration rates and a consistent tendency for immigration rates to depend underproportionally on local densities. Potential implications of the shape of the dispersal distribution for the spread of invading organisms were investigated and compared with previous results. It is shown that the wave speed, for a given dispersal standard deviation, depends only to some extent on leptokurtosis, provided that the intrinsic growth rate of the population is moderate or small. In estimating the dispersal standard deviation, however, incorrect assumptions about the degree of leptokurtosis can lead to a large bias in estimation and predictions.