The most efficient tuning you can do is not to alter what works well. As they say, "If it ain't broke, don't fix it." This may seem obvious, but the temptation to tweak something just because you have thought of an improvement has a tendency to override this obvious statement.
The second most efficient tuning is to discard work that doesn't need doing. It is not at all uncommon for an application to be started with one set of specifications and to have some of the specifications change over time. Many times the initial specifications are much more generic than the final product. However, the earlier generic specifications often still have their stamps in the application. I frequently find routines, variables, objects, and subsystems that are still being maintained but are never used and never will be used because some critical aspect is no longer supported. These redundant parts of the application can usually be chopped without any bad consequences, often resulting in a performance gain.
In general, you need to ask yourself exactly what the application is doing and why. Then question whether it needs to do it in that way, or even if it needs to do it at all. If you have third-party products and tools being used by the application, consider exactly what they are doing. Try to be aware of the main resources they use (from their documentation). For example, a zippy DLL (shared library) that is speeding up all your network transfers is using some resources to achieve that speedup. You should know that it is allocating larger and larger buffers before you start trying to hunt down the source of your mysteriously disappearing memory. Then you can realize that you need to use the more complicated interface to the DLL that restricts resource usage rather than a simple and convenient interface. And you will have realized this before doing extensive (and useless) object profiling because you would have been trying to determine why your application is being a memory hog.
When benchmarking third-party components, you need to apply a good simulation of exactly how you will use those products. Determine characteristics from your benchmarks and put the numbers into your overall model to determine if performance can be reached. Be aware that vendor benchmarks are typically useless for a particular application. Break your application down into a hugely simplified version for a preliminary benchmark implementation to test third-party components. You should make a strong attempt to include all the scaling necessary so that you are benchmarking a fully scaled usage of the components, not some reduced version that reveals little about the components in full use.