Summary: Let \(X_ 1,...,X_ n\) be a random sample from a normal distribution with mean \(\theta\) and variance \(\sigma^ 2\). The problem is to etimate \(\theta\) with the loss function \[ L(\theta,e)=v(e-\theta)\quad where\quad v(x)=b(\exp (ax)-ax-1) \] and where a, b are constants with \(b>0\), \(a\neq 0\). A. Zellner [J. Am. Stat. Assoc. 81, 446-451 (1986; Zbl 0603.62037)], showed that \(\bar X-\sigma 2a/2n\) dominates \(\bar X\) and hence \(\bar X\) is inadmissible. The question of what values of c and d render \(c\bar X+d\) admissible is studied here.