Quantum mechanics/molecular mechanics (QM/MM) is the method of choice for atomistic simulations of large systems that can be partitioned into active and environmental regions. Adaptive-partitioning (AP) methods extend the applicability of QM/MM, allowing active regions to change during the simulation. AP methods achieve continuous potential energy surface (PES) by introducing buffer regions in which atoms have both QM and MM characters. Most of the existing AP-QM/MM methods require multiple QM calculations per time step, which can be expensive for systems with many atoms in buffer regions. Although one can lower the computational cost by grouping atoms into fragments, this may not be possible for all systems, especially for applications in covalent solids. The SISPA method [Field, J. Chem. Theory Comput., 2017, 13, 2342] differs from other AP-QM/MM methods by only requiring one QM calculation per time step, but it has the flaw that the QM charge density and wavefunction near the buffer/MM boundary tend to those of isolated atoms/fragments. Besides, regular QM/MM methods for treating covalent bonds cut by the QM/MM boundary are incompatible with SISPA. Due to these flaws, SISPA in its original form cannot treat covalently bonded systems properly. In this work, I show that a simple modification to the SISPA method improves the treatment of covalently bonded systems. I also study the effect of correcting the charge density in SISPA by developing a density-corrected pre-scaled algorithm. I demonstrate the methods with simple molecules and bulk solids.