  I develop n-site cluster approximations for a stochastic sandpile in one
dimension. A height restriction is imposed to limit the number of states: each
site can harbor at most two particles (height z_i \leq 2). (This yields a
considerable simplification over the unrestricted case, in which the number of
states per site is unbounded.) On the basis of results for n \leq 11 sites, I
estimate the critical particle density as zeta_c = 0.930(1), in good agreement
with simulations. A coherent anomaly analysis yields estimates for the order
parameter exponent [beta = 0.41(1)] and the relaxation time exponent (nu_||
\simeq 2.5).
