The dynamic control of the dielectric response in magnetoelectric (ME) nanocomposites (NCs) renders an entire additional degree of freedom to the functionality of miniaturized magnetoelectronics and spintronics devices. In composite materials, the ME effect is realized by using the concept of product properties. Through the investigation of the microwave properties of a series of BaTiO3/Ni NCs fabricated by compaction of nanopowders, we present experimental evidence that the compaction (uniaxial) pressure in the range of 33-230 MPa significantly affects the ME features. We report here data for only one composition (17.1 vol.% of Ni in the BaTiO3/Ni NC sample). Our findings revealed that the ME coupling coefficient exhibits a large enhancement for specific values of the Ni volume fraction and compaction pressure. Overall, these observations are considered to be evidence of stress-induced microstructural changes under pressure that strongly affect the elastic interaction between the magnetostrictive and piezoelectric phases in these NCs. These results have a potential technological impact for designing precise tunable ME NCs for microwave devices such as tunable phase shifters, resonators, and delay lines.