Rings over which proper cyclics are injective (called PCI-rings) have been characterized by C. Faith [Pac. J. Math. 45, 97-112 (1973; Zbl 0258.16024)] and R. F. Damiano [Proc. Am. Math. Soc. 77, 11-14 (1979; Zbl 0425.16022)] as semisimple artinian rings or simple right noetherian, right hereditary domains over which each proper cyclic module is semisimple. Dinh Van Huynh, S. K. Jain and S. R. López-Permouth [J. Algebra 184, No. 2, 789-794 (1996; 856.16020)] showed that simple rings over which proper cyclics are quasi-injective (called PCQI-rings) are the same as simple PCI-rings. The authors extend the result by showing that a simple ring over which proper cyclics are continuous is indeed a PCI-ring. The proof has a strong computational flavor, as it is based on looking at the form of the cyclic modules involved and on the precise computation of the intersection of certain pairs of modules.