The detailed theoretical investigation into the spectral phase and intrinsic dispersion of high-order harmonics generated by monocycle pumping [a $1.93\mathrm{fs}$ ( $T_0$ ), $580\mathrm{nm}$ ( ${\lambda }_0$ ), $1.7–2.0\times {10}^{15}\mathrm{W}/{\mathrm{cm}}^2$ ( $I_0$ ), Gaussian-shaped pulse] showed that it is significantly important for further shortening of isolated attosecond pulses to select the spectral region that has the minimum intrinsic group-delay dispersion and higher-order dispersion in the middle region of the plateau, other than that close to the cutoff where the harmonic intensity drops rapidly. We demonstrated that the selection is carried out directly from the harmonic-order-dependent electron-recombination time, which is obtained from the simple semiclassical method and can be measured by experiment. Consequently, we found that monocycle pumping can generate efficiently $68\mathrm{as}$ isolated pulses without chirp compensation as well as tunable (115 to $150\mathrm{eV}$ ), sub $70\mathrm{as}$ pulses from He atoms by tuning the carrier-envelope phase. Particularly, nearly transform-limited $43\mathrm{as}$ isolated pulses can be produced under the double-intensity ( $I_{\text{pump}}=2I_0$ ) and double- wavelength ( ${\lambda }_{\text{pump}}=2{\lambda }_0$ , $T_{\text{pump}}=2T_0$ ) pump. These results were also confirmed by the saddle-point analysis based on the Lewenstein model.