Distributed service applications make heavy use of clouds and multi-clouds, and must (i) meet service quality goals (e.g. response time) while (ii) satisfying cloud resource constraints and (iii) conserving power. Deployment algorithms must (iv) provide a solution meeting these requirements within a short time to be useful in practice. Very few existing deployment methods address the first three requirements, and those that do take too long to find a deployment. The Low-Power Multi-Cloud Application Deployment (LPD) algorithm fills this gap with a low-complexity heuristic combination of generalized graph partitioning between clouds, bin-packing within each cloud and queueing approximations to control the response time. LPD has no known competitor that quickly finds a solution that satisfies response time bounds. A host execution time approximation for contention is fundamental to achieving sufficient solution speed. LPD is intended for use by cloud managers who must simultaneously manage hosts and application deployments and plan capacity to offer services such as Serverless Computing.On 104 test scenarios deploying up to 200 processes with up to 240 replicas (for scaling), LPD always produced a feasible solution within 100 s (within 20 seconds in over three-quarters of cases). Compared to the Mixed Integer Program solution by CPLEX (which took a lot longer and was sometimes not found) LPD solutions gave power consumption equal to MIP in a third of cases and within 6% of MIP in 95% of cases. In 93% of all 104 cases the power consumption is within 20% of an (unachievable) lower bound.LPD is intended as a stand-alone heuristic to meet solution time restrictions, but could easily be adapted for use as a repair mechanism in a Genetic Algorithm.