The primary instability of salt fingers in an unbounded fluid with uniform vertical salinity/temperature $(\skew4\bar{S}_z^\ast/\skew2\bar{T}_z^\ast)$ gradients consists of a vertically $(z)$ uniform ‘elevator’ mode, amplifying exponentially in time. We compute the $z$-wavelength $(h_{0})$ of the fastest growing secondary instability by integrating a system of linear partial differential equations (PDEs) with time-dependent and horizontally periodic coefficients. It is suggested that this instability limits the amplitude of the primary mode and $h_{0}\skew4\bar{S}_z^\ast$ determines the value of the statistically steady r.m.s. salinity fluctuation $(S^\prime)$. Comparisons of $h_{0}$ with ${\langle{\overline{({S}')^2}}\rangle^{1/2}}/{\skew4\bar{S}_z^\ast}$ are made using direct numerical simulations (DNS), and our theory for the vertical salt/heat flux is also given and compared with the DNS.