We consider the total dividends paid prior to ruin under a threshold strategy. We investigate a class of Sparre-Andersen risk processes and its associated class of delayed risk processes with rational-distributed inter-claim times. With the presence of a constant dividend barrier, we present a structure of integro-differential equation, which is applicable to numerous quantities such as the Gerber–Shiu function, the maximum surplus, etc. Finally, we study the fraction of time of dividends payment prior to ruin. This is of interest to an investor who wants to know how often to expect dividends.