Using pdflatex, the command
$e^{a\overbrace{+b+c}}$
results in a bigger size font of the part +b+c under the brace. If I do:
$e^{a\overbrace{\scriptstyle +b+c}}$
the size of +b+c is fixed but the size of the brace is still wrong: the brace has the same size than before but, since the interior font is now smaller, white spaces appear.
Can we fix this?
NOTE: This question can be considered a duplicated of Underbrace and Subscripts. However, the solutions in that question do not tackle the brace size problem. I don't have enough repuation to add this as a comment there and I don't think it is a good idea to add an answer that is rather a question.
NOTE2: Using mathtools does not change the problem.

