In several papers, a solar cycle (SC) influence in the lower atmosphere has been linked to the Quasi-biennial Oscillation (QBO), which is generated primarily by small-scale gravity waves. Salby and Callaghan (J. Clim. 2000) analyzed the QBO observations covering more than 40 years and found that it contains a relatively large SC signature at 20 km. Following up on a study with the 2D version of our global-scale Numerical Spectral Model (NSM), we recently initiated a 3D study in which we simulated the QBO under the influence of the SC. Choosing a representative SC period of 10 years, the relative variations of the radiative forcing is taken to vary logarithmically from 0.2% at the surface to 2% at 50 km to 20% at 100 km and above, consistent with solar observations. Initial results indicate that the NSM can produce a relatively large modulation of the QBO related to the SC, and we discuss ideas how the effect might be generated. But our results must be considered preliminary. Our model needs to simulate many solar cycles to reach steady state, and we must carry out parametric studies with improved vertical and temporal resolutions to determine whether the effect is real and the results are robust. Numerical experiments are needed to explore and more fully understand the mechanism that may amplify the SC influence. And it will be important that we deal with the quasi-decadal oscillations that can be generated internally by the QBO interacting with the seasonal cycles, which may in turn overshadow, or aid, the SC influence.