The mean-lifetimes, \ensuremath{\tau}, of various medium-spin excited states in $^{103}\mathrm{Pd}$ and $^{106,107}\mathrm{Cd}$ have been deduced using the Recoil Distance Doppler Shift technique and the Differential Decay Curve Method. In $^{106}\mathrm{Cd}$, the mean-lifetimes of the ${I}^{\ensuremath{\pi}}={12}^{+}$ state at ${E}_{x}=5418$ keV and the ${I}^{\ensuremath{\pi}}={11}^{\ensuremath{-}}$ state at ${E}_{x}=4324$ keV have been deduced as 11.4(17)ps and 8.2(7)ps, respectively. The associated ${\ensuremath{\beta}}_{2}$ deformation within the axially-symmetric deformed rotor model for these states are 0.14(1) and 0.14(1), respectively. The ${\ensuremath{\beta}}_{2}$ deformation of 0.14(1) for the ${I}^{\ensuremath{\pi}}={12}^{+}$ state in $^{106}\mathrm{Cd}$ compares with a predicted ${\ensuremath{\beta}}_{2}$ value from total Routhian surface (TRS) calculations of 0.17. In addition, the mean-lifetimes of the yrast ${I}^{\ensuremath{\pi}}={\frac{15}{2}}^{\ensuremath{-}}$ states in $^{103}\mathrm{Pd}$ (at ${E}_{x}=1262$ keV) and $^{107}\mathrm{Cd}$ (at ${E}_{x}=1360$ keV) have been deduced to be 31.2(44)ps and 31.4(17)ps, respectively, corresponding to ${\ensuremath{\beta}}_{2}$ values of 0.16(1) and 0.12(1) assuming axial symmetry. Agreement with TRS calculations are good for $^{103}\mathrm{Pd}$ but deviate for that predicted for $^{107}\mathrm{Cd}$.