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In portfolio compression, market participants (banks, organizations, companies, financial agents) sign contracts, creating liabilities between each other, which increases the systemic risk. Large, dense markets commonly can be compressed by reducing obligations without lowering the net notional of each participant (an example is if liabilities make a cycle between agents, then it is possible to reduce each of them without any net notional changing), and our target is to eliminate as much excess notional as possible in practice (excess is defined as the difference between gross and net notional). A limiting factor that may reduce the effectiveness of the compression can be the preferences and priorities of compression participants, who may individually define conditions for the compression, which must be considered when designing the clearing process, otherwise, a participant may bail out, resulting in the designed clearing process to be impossible to execute. These markets can be well-represented with edge-weighted graphs. In this paper, I examine cases when preferences of participants on behalf of clearing are given, e.g., in what order would they pay back their liabilities (a key factor can be the rate of interest) and I show a clearing algorithm for these problems. On top of that, since it is a common goal for the compression coordinating authority to maximize the compressed amount, I also show a method to compute the maximum volume conservative compression in a network. I further evaluate the possibility of combining the two models. Examples and program code of the model are also shown, also a0 pseudo-code of the clearing algorithms.