The properties of the form factors describing the rare CP conserving decay modes $K \to \pi l^+ l^-$, $(K,\pi) = (K^\pm,\pi^\pm)$ or $(K_S,\pi^0)$, $l=e,\mu$, are addressed. First, a full two-loop representation of the corresponding form factors in the low-energy expansion is constructed. Next, the contribution from pi-pi intermediate states is considered from a dispersive point of view. Particular attention is given to the matching with the short-distance behaviour of the form factors. Finally, phenomenological aspects of this study are discussed.