Let ${B_{z}^{\alpha, \beta},z\in[0,T]^{2} }$ be a $d$-dimensional fractional Brownian sheet with Hurst parameters $(\alpha, \beta)\in(0,\frac{1}{2})^{2}$. We consider the problem of parameter estimation for the drift of fractional Brownian sheet $B^{\alpha,\beta}$ and construct superefficient James–Stein estimators which dominate, under the usual quadratic risk, the natural maximum likelihood estimator.