It has been observed that a swollen L-alpha phase (Surfactant : Cetylpyridinium Chloride; Cosurfactant : Hexanol; Solvent : Brine) keeps (at least) metastable under the addition of a Dilute quantity of a neutral, flexible polymer (Polyacrylamide) in brine in a large domain of concentration (Ref. 3a), however the periodicity of the lamellar phase suffers a strong decrease. We explain this phenomenon by a privileged swelling of the polymer coils, under the effect of an osmotic pressure localized in the coil region.