Let (X,\(\Omega\),f(x;\(\omega)\)) be a parametric statistical model and consider a mapping \(\lambda\) :\(\Omega\) \(\to \Lambda \equiv \lambda (\Omega)\). In the paper a definition of partial sufficiency (''L- sufficiency'') with respect to \(\lambda\) (\(\omega)\) is introduced as follows: t(x) is L-sufficient if and only if \(t(x_ 0)=t(x_ 1)\Rightarrow {\tilde \ell}(\lambda;x_ 0)={\tilde \ell}(\lambda;x_ 1)\) where \[ {\tilde \ell}(\lambda;x)=\sup_{\omega:\lambda (\omega)=\lambda}\log (L(\omega;x)/\sup_{\omega \in \Omega}L(\omega;x)) \] and L(\(\omega\) ;x) is the likelihood function. For example, let \((x_ 1,y_ 1),...,(x_ n,y_ n)\) be a sample from a bivariate normal population \[ N[(0,0);\quad \left( \begin{matrix} \sigma^ 2_ 1\\ \rho \sigma_ 1\sigma_ 2\end{matrix} \begin{matrix} \rho \sigma_ 1\sigma_ 2\\ \sigma^ 2_ 2\end{matrix} \right)]; \] then, as it is proved, the minimal L-sufficient statistic for \(\rho\) is \[ t=\sum_{i}x_ iy_ i/\sqrt{\sum_{i}x^ 2_ i\sum_{i}y^ 2_ i}. \] Several further examples of minimal L-sufficiency are shown. The relations to definitions of partial sufficiency previously given by \textit{D. A. S. Fraser} [Ann. Math. Stat. 27, 838-842 (1956; Zbl 0073.149)] and \textit{G. A. Barnard} [J. R. Stat. Soc., Ser. B 25, 124-127 (1963; Zbl 0118.144)], respectively, are discussed..