Semianalytical methods for the determination of first-order rate constant distributions are discussed. In general the expression for the overall decay function is an integral equation based on the local decay function and the distribution function. The analytical expressions of the distribution function obtained by inversion of the integral equation are a series of derivatives of the overall decay function. The higher the order of the approximation, the more derivatives are required. The most common method is based on the Laplace transform technique; newly derived are the coefficients for the third-order method. The second method is due to Schwarzl and Staverman, it provides a general scheme to find a distribution function from an integral equation and has been used here to obtain an expression for the rate constant distribution. The advantage of this method is that it provides a weighting function that maps the true distribution into its approximation; i.e., it visualizes the quality of the approximation. The third method is newly developed. It uses an approximation of the local decay function to solve the integral equation for the distribution function. The local decay function approximation br LODA method provides a physical interpretation of the approximation involved in obtaining the distribution by showing the function that approximates the true local decay function. The three methods are compared on the basis of two synthetic data sets, one composed of exact data and one of nonexact data. For nonexact data presmoothing of the data is required. For this purpose a smoothing spline technique is applied in which the smoothing parameter is obtained objectively by generalized cross validation in combination with physical constraints. It is shown that the newly developed LODA-G2 method, which needs the first and second derivative of the overall decay function, combines a good resolution with a relatively low sensitivity to experimental error.