Making a payment in a privacy-aware payment channel network is achieved by trying several payment paths until one succeeds. With a large network, such as the Lightning Network, a completion of a single payment can take up to several minutes. We introduce a network imbalance measure and formulate the optimization problem of improving the balance of the network as a sequence of rebalancing operations of the funds within the channels along circular paths within the network. As the funds and balances of channels are not globally known, we introduce a greedy heuristic with which every node despite the uncertainty can improve its own local balance. In an empirical simulation on a recent snapshot of the Lightning Network we demonstrate that the imbalance distribution of the network has a Kolmogorov-Smirnoff distance of 0.74 in comparison to the imbalance distribution after the heuristic is applied. We further show that the success rate of a single unit payment increases from 11.2% on the imbalanced network to 98.3% in the balanced network. Similarly, the median possible payment size across all pairs of participants increases from 0 to 0.5 mBTC for initial routing attempts on the cheapest possible path. We provide an empirical evidence that routing fees should be dropped for proactive rebalancing operations. Executing 4 different strategies for selecting rebalancing cycles lead to similar results indicating that a collaborative approach within the friend of a friend network might be preferable from a practical point of view