We demonstrate, both theoretically and experimentally, that the excitation efficiency of triple-quantum coherences in 3QMAS experiments of spin 5/2 systems can be enhanced by manipulating the population of the external satellites prior to hard pulse excitation of the 3Q coherence. Theoretically, a 67% or 33% increase can be achieved by respectively inverting or saturating the outer satellites. Experimentally an increase of approximately 25% is obtained. The manipulation of the external satellites is achieved using time-dependent amplitude-modulated pulses. It is demonstrated for the mineral andalusite that combining enhancements in 3Q-excition and 3Q --> 1Q conversion leads to 3QMAS spectra with well-defined line shapes for sites experiencing strongly different quadrupolar interactions.