Cloud providers handle substantial number of requests to create and delete virtual machines (VMs) on a daily basis, where the unknown sequence of requests eventually leads to resource fragmentation. To mitigate this issue, periodic consolidation of VMs into fewer number of physical hosts is an important cost-saving procedure, closely related to the vector bin-packing problem. In this paper, we propose the BalCon algorithm for consolidation that steadily reduces the number of active hosts and keeps migration costs low. BalCon classifies the cluster's state and selects one of three heuristics to balance resources for superior consolidation. To evaluate BalCon's performance with respect to optimality, we introduce integer programming models. BalCon finds 99.7% of the optimal solutions for over 750 problem instances. This outstanding result was achieved due to the Force Step of our algorithm, which is the key improvement detail for common heuristics. We compare BalCon with a modified Sercon heuristic using Huawei and synthetic datasets with two resources for allocation.