Constrained cube gradient mining is an important mining task and its goal is to extract the pairs of gradient-probe cell satisfy the gradient constraint from a data cube. However, previous work are explored for a general data cube. In this paper, the problem of the mining constrained cube gradient for a condensed cube is studied. An algorithm named as eLiveSet for the problem is developed through the extension of the existing efficient mining algorithm LiveSet-driven. The experimental results show that the algorithm is more effective than the existing algorithm on the performance of mining constrained cube gradient.