This work addresses the piezoelectric induced reduction of quality factor in fully-printed metal-insulator-metal (MIM) barium strontium titanate (BST) thick film varactors designed for high power operation. An acoustically optimized varactor design is presented and compared to a non-optimized high-power varactor. The design is utilized to present a narrowband acoustic suppression technique based on defined weights. The acoustically optimized varactor consists of 162 varactor cells in a capacitive matrix. The cells in the matrix are interconnectable allowing for a variable unbiased capacitance and power rating. Due to this setup, surface acoustic waves are interrupted, and the reduced size of the cells allows for a reduced BST layer thickness, shifting the acoustic resonance away from the operational frequency. Therefore, an inverted behavior in comparison to the high-power varactor is observed with an increasing quality factor with biasing voltage. Compared to the high-power varactor, the acoustically optimized varactor design shows a 40% increased quality factor in biased state. By applying the narrowband acoustic suppression technique, an increase in quality factor of 145% is achieved compared to the unsuppressed design. In comparison to the high-power varactor, the acoustical suppressed design shows an increase in quality factor of 480% at the first acoustic resonance frequency.