This paper analyzes the interconnections of underreported earnings, savings and oldage pension with the help of a most simple, elementary model. The workers can be divided into three groups: 1) well-paid who report their full earnings, 2) well-paid who report only the minimum earnings (evaders) and 3) the poorly paid. We assume that the evaders save a significant part of their hidden earnings for their old age. We compare three pension systems of equal size: (i) the proportional, (ii) the proportional plus basic pension and (iii) the proportional with means testing. Our major result is as follows: if the evaders can be recognized and excluded, then the means-tested system is superior to the basic system.