  Elaborating on ideas of Elkies, we show how recursive equations for towers of
Drinfeld modular curves $(X_0(P^n))_{n\ge 0}$ for $P\in \mathbb F_q[T]$ can be
read of directly from the modular polynomial $\Phi_P(X,Y)$ and how this
naturally leads to recursions of depth two. Although the modular polynomial
$\Phi_T(X,Y)$ is not known in general, using generators and relations given by
Schweizer, we find unreduced recursive equations over $\mathbb F_q(T)$ for the
tower $(X_0(T^n))_{n\ge 2}$ and of a small variation of it (its partial Galois
closure). Reducing at various primes, one obtains towers over finite fields,
which are optimal, i.e., reach the Drinfeld--Vladut bound, over a quadratic
extension of the finite field. We give a proof of the optimality of these
towers, which is elementary and does not rely on their modular interpretation
except at one point. We employ the modular interpretation to determine the
splitting field of certain polynomials, which are analogues of the Deuring
polynomial. For these towers, the particular case of reduction at the prime
$T-1$ corresponds to towers introduced by Elkies and Garcia--Stichtenoth.
