In a cell-free massive MIMO (CFmMIMO) network with a daisy-chain fronthaul, the amount of information that each access point (AP) needs to communicate with the next AP in the chain is determined by the location of the AP in the sequential fronthaul. Therefore, we propose two sequential processing strategies to combat the adverse effect of fronthaul compression on the sum of users' spectral efficiency (SE): 1) linearly increasing fronthaul capacity allocation among APs and 2) Two-Path users' signal estimation. The two strategies show superior performance in terms of sum SE compared to the equal fronthaul capacity allocation and Single-Path sequential signal estimation.