When the sample variables X_i are exponentially distributed with mean EX_ii=?, then, for ?, a fixed-width confidence estimation observing the confidence level for all values of ?>0 is stated. It can be seen that the asymptotic effectiveness of the procedure obtained is no worse than that achieved by a stopping rule derived from asymptotic theory, whose disadvantages are, however, avoided (the cover probability failing very below the confidence level for finite values of ?)