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This thesis shows how supercompilation, a powerful technique for transformation and analysis of functional programs, can be effectively applied to a call-by-need language. Our setting will be core calculi suitable for use as intermediate languages when compiling higher-order, lazy functional programming languages such as Haskell. We describe a new formulation of supercompilation which is more closely connected to operational semantics than the standard presentation. As a result of this connection, we are able to exploit a standard Sestoft-style operational semantics to build a supercompiler which, for the first time, is able to supercompile a call-by-need language with unrestricted recursive let bindings. We give complete descriptions of all of the (surprisingly tricky) components of the resulting supercompiler, showing in detail how standard formulations of supercompilation have to be adapted for the call-by-need setting. We show how the standard technique of generalisation can be extended to the call-by-need setting. We also describe a novel generalisation scheme which is simpler to implement than standard generalisation techniques, and describe a completely new form of generalisation which can be used when supercompiling a typed language to ameliorate the phenomenon of supercompilers overspecialising functions on their type arguments. We also demonstrate a number of non-generalisation-based techniques that can be used to improve the quality of the code generated by the supercompiler. Firstly, we show how let-speculation can be used to ameliorate the effects of the work-duplication checks that are inherent to call-by-need supercompilation. Secondly, we demonstrate how the standard idea of ‘rollback’ in supercompilation can be adapted to our presentation of the supercompilation algorithm. We have implemented our supercompiler as an optimisation pass in the Glasgow Haskell Compiler. We perform a comprehensive evaluation of our implementation on a suite of standard call-by-need benchmarks. We improve the runtime of the benchmarks in our suite by a geometric mean of 42%, and reduce the amount of memory which the benchmarks allocate by a geometric mean of 34%.