Adjusting height of left(, right), etc

For aesthetic reasons, I prefer the aspect of the first equation in the following example to the second.

begin{align}
Big|sum_{n=1}^infty f_nBig|_p^p&=int_XBig|sum_{n=1}^infty f_nBig|^pmathrm{d}mu=int_Xbig(lim_{ntoinfty}s_n,big)mathrm{d}mu,
left|sum_{n=1}^infty f_nright|_p^p&=int_Xleft|sum_{n=1}^infty f_nright|^pmathrm{d}mu=int_Xleft(lim_{ntoinfty}s_n,right)mathrm{d}mu.
end{align}

I think it goes without saying, but what I want is for the parentheses to fit the height of the operators but leave out the subscripts and superscripts.

The problem. I want to modify a previous document written with style (2) and convert it to style (1). I’m afraid I’ll have to do it by hand, since there are going to be numerous left( and right) in some equations that won’t need to be modified.

The question. Is there a way to redefine left(, right), left[, etc. to adapt them to this behavior?