Quantum dissipative effects are usually studied by the system-plus-reservoir (SPR) model, which makes quantization possible by considering the whole energy-conserving system, while the reservoir's degrees of freedom, assumed to be harmonic, can be "traced out" by the path-integral technique, leading to a formulation that only includes the dynamical variables of the system of interest. In the standard SPR model the environment is only coupled with the system's coordinates and turns out to generally quench their quantum fluctuations. However, there are physical systems coupled with an environment whose "coordinates" and "momenta" can be completely interchangeable (e.g., magnets), so an SPR coupling must symmetrically affect both canonical variables. We studied different variants of such a general environmental coupling in the case of a harmonic oscillator. It is found that quantum fluctuations are generally enhanced by environmental coupling, with an unexpected nonmonotonic behavior. This leads one to speculate about the possibility that spin-lattice coupling could drive the two-dimensional Heisenberg antiferromagnet to reach its quantum-critical point.