Age trajectories of total mortality represent an irreplaceable source of information about the relationship between mortality and age. Total mortality includes death from external causes. Age affects mortality from all diseases differently than it affects mortality from external causes. This study examines mortality with external causes excluded. The resulting category of all-diseases is examined as a helpful tool to better understand the relationship between mortality and age. Age trajectories of all-diseases mortality are studied in Austria, the Czech Republic, Hungary, Poland, and Slovakia. Resulting age trajectories of all-diseases mortality show a strong minimum that is hidden in all-causes mortality. Two deterministic models fit the resulting age trajectories of mortality on either side of the strong mortality minimum. The inverse proportion between mortality and age is used from birth to the age when all-diseases mortality reaches the minimum value. The Gompertz relationship fits age trajectories of all-diseases mortality in 93 out of 183 cases. When extended with a small quadratic element, the Gompertz model is used to fit the remaining 90 cases.