Let Pt be the Poisson kernel. We study the following Lp inequality for the Poisson integral P f(x, t) = (Pt ∗ f)(x) with respect to a Carleson measure µ: L p(R n+1 + ,dµ) ≤ cp,nκ(µ) 1 p L p(Rn,dx) , where 1 < p < ∞ and κ(µ) is the Carleson norm of µ. It was shown by Verbitsky [V] that for p > 2 the constant cp,n can be taken to be independent of the dimension n. We show that c2,n = O((log n) 1 2 ) and that cp,n = O(n 1 p − 1 2 ) for 1 < p < 2 as n → ∞. We observe that standard proofs of this inequality rely on doubling properties of cubes and lead to a value of cp,n that grows exponentially with n. P f