In Compressive Sensing (CS) of sparse signals, standard ℓ1 minimization can be effectively replaced with Weighted ℓ1 -minimization (Wℓ1) if some information about the signal or its sparsity pattern is available. If no such information is available, Re-Weighted ℓ1 -minimization (ReWℓ1) can be deployed. ReW ℓ1 solves a series of W ℓ1 problems, and therefore, its computational complexity is high. An alternative to ReW ℓ1 is the Greedy Pursuits Assisted Basis Pursuit (GPABP) which employs multiple Greedy Pursuits (GPs) to obtain signal information which in turn is used to run W ℓ1. Although GPABP is an effective fusion technique, it adapts a binary weighting strategy for running W ℓ1, which is very restrictive. In this article, we propose a gradual weighting strategy for W ℓ1, which handles the signal estimates resulting from multiple GPs more effectively compared to the binary weighting strategy of GPABP. The resulting algorithm is termed as Greedy Pursuits assisted Weighted ℓ1 -minimization (GP-W ℓ1). For GP-W ℓ1, we derive the theoretical upper bound on its reconstruction error. Through simulation results, we show that the proposed GP-W ℓ1 outperforms ReW ℓ1 and the state-of-the-art GPABP. © 2018 IEEE.