Abstract: Reactive synthesis from high-level specifications that combine {\em hard} constraints expressed in Linear Temporal Logic ($\ltl$) with {\em soft} constraints expressed by discounted-sum (DS) rewards has applications in planning and reinforcement learning. An existing approach combines techniques from $\ltl$ synthesis with optimization for the DS rewards but has failed to yield a sound algorithm. An alternative approach combining $\ltl$ synthesis with satisficing DS rewards (rewards that achieve a threshold) is sound and complete for integer discount factors, but, in practice, a fractional discount factor is desired. This work extends the existing satisficing approach, presenting the first sound algorithm for synthesis from $\ltl$ and DS rewards with fractional discount factors. The utility of our algorithm is demonstrated on robotic planning domains.