our theoretical analysis of the bound state spectra in three-electron atoms and ions. The analysis of the bound state spectra in similar atomic systems is based on the use of fast-convergent variational expansions which provide high numerical accuracy not only for the ground and some low-lying rotationally excited states, but for all excited states in few-electron atom(s) and ions. This expansion is the Hylleraas-Configuration Interaction (Hy-CI) wave function, proposed by Sims and Hagstrom [@SH1; @SH2], which we have used to determine the $S$-, $P$-, $D$-states of the C$^{3+}$ and F$^{6+}$ ions and the Configuration Interaction (CI) wave function with Slater orbitals and $LS$ configurations for the states of higher symmetry $F$, $G$, $H$, $I$, $K$, $L$, $M$, $N$ and states with $L=20$. Note that the Hy-CI is general for any symmetry. At the moment in our computer program the kinetic energy integrals are restricted to $l = 3$, work is in progress to generalize our code for $l \ge 3$. Nevertheless, the CI wave function leads to very good results for states with quantum number $L \ge 3$. The Hy-CI and CI wave functions can be summarized in the following expression: $$\Psi =\sum_{p=1}^NC_p\Phi _p,\qquad \Phi _p=\hat{O}(\hat{L}^2)\hat{\mathcal{A}}\psi _p\chi$$ $N$ is the 