  It has recently been suggested that the discrepancy between the "long" and
"short" distance moduli of the Large Magellanic Cloud (LMC), as inferred from
the properties of the Cepheid and RR Lyrae variables, respectively, might be
due to the action of "third parameters" between the Galaxy and the LMC, which
would make the RR Lyraes in the old LMC globular clusters brighter than their
Galactic counterparts by $\simeq 0.3 {mag}$. Through analysis of the RR Lyrae
pulsation properties, we show that this idea is not supported by the available
data. A satisfactory explanation of the problem has yet to be found.
