Current serverless offerings give users a limited degree of flexibility for configuring the resources allocated to their function invocations by either coupling memory and CPU resources together or providing no knobs at all. These configuration choices simplify resource allocation decisions on behalf of users, but at the same time, create deployments that are resource inefficient. In this paper, we take a principled approach to the problem of resource allocation for serverless functions, allowing this choice to be made in an automatic way that leads to the best combination of performance and cost. In particular, we systematically explore the opportunities that come with decoupling memory and CPU resource allocations and also enabling the use of different VM types. We find a rich trade-off space between performance and cost. The provider can use this in a number of ways: from exposing all these parameters to the user, to eliciting preferences for performance and cost from users, or by simply offering the same performance with lower cost. This flexibility can also enable the provider to optimize its resource utilization and enable a cost-effective service with predictable performance. Our results show that, by decoupling memory and CPU allocation, there is potential to have up to 40% lower execution cost than the preset coupled configurations that are the norm in current serverless offerings. Similarly, making the correct choice of VM instance type can provide up to 50% better execution time. Furthermore, we demonstrate that providers can utilize different instance types for the same functions to maximize resource utilization while providing performance within 10-20% of the best resource configuration for each respective function.