A typical resource constrained environment is restrained in terms of availability of resources such as skilled personnel, equipments, power and Internet connectivity. Designing privacy-based service-oriented architectures therefore requires re-adapting existing solutions to cope with the constraints of the environment. In this paper, we consider the case of mobile crime-reporting systems that have emerged as an effective and efficient data collection method in developing countries. Analyzing the data, can be helpful in addressing crime but, law enforcement agencies in resource-constrained contexts typically do not have the expertise required to handle these tasks. A possible cost-effective strategy is thus to outsource the data analytics operations to third-party service providers. However, the sensitivity of the data makes privacy an important consideration. In this paper we propose a two-pronged approach to addressing the issue of privacy in outsourcing crime data in resource constrained contexts. We build on this in the second step to propose a streaming data anonymization algorithm to analyse reported data based on occurrence rate rather than at a preset time on a static repository. Results from our prototype implementation and usability tests indicate that having a usable and covet crime-reporting application encourages users to declare crime occurrences and anonymizing streaming data contributes to faster crime resolution times.