  We analyse the effect of thermal fluctuations on the elastic constants of the
decoupled lamellar phase of tethered, crystalline membranes. Using a
momentum-shell renormalization group technique, we show that the smectic-A
-like compressional elastic constant, the in-plane Lam\'{e} coefficients, and
the cross-coupling elastic constant vanish as (\ln q)^{- a} whereas the bend
elastic constant diverges as (\ln q)^{b}, with a, b > 0, as the wavenumber q
tends to zero. The exponents a and b satisfy the relation a + 3b = 2.
