Without agreeing or disagreeing with Joe's comment above, there is a data point you can collect although it won't easy and it will certainly add overhead to your process.
For each bug detected you will surely report the phase where it was introduced, either by tracing back date ranges or simply by adding a field called something like "detected on phase". You can also add a field that is filled by the developer whenever he understands the issue called something like "entered on phase" where he will try to trace back the change that caused this issue.
Then you can calculate:
Defect Removal Efficiency in Round 1 =
Defects found in round 1/[Defects found in Round 1 + (Defects found in Round 2 - Defects found in Round 2 entered in Round 2)]
If you ask me, this is at least a partial waste of time (you would learn more by investing this time in writing down even a partial root-cause-analysis); but then again this may be out of your influence zone.
In any case, you asked for a solution and this is mine...