Can you take away the noise and pull up the voice?

In my day job, I regularly get phone calls and emails from people who want to know basically the same thing - might it be possible to take away the noise and pull up the voice on a particular audio recording? Of course, without hearing the recording first there is only so much I can say. That being said, what is really needed at that point is an indication of whether it is a lost cause or not before going to the time and effort of submitting the recording for a formal evaluation.

So, how can one legitimately respond to such a question? First, I ask a few questions, such as:

• Was it legally recorded? If yes, was it a one-party or two-party consent? If no, they might need to be contacting legal counsel and not me.
  
• Is it a criminal, civil, or professional matter? If criminal, have they already contacted the appropriate authorities?
• What kind of recorder is it (e.g. pocket recorder, cassette deck, or answering machine)?
• What is the noise/interference like (e.g. hum, hiss, another talker, music, machinery, pops/clicks, or mobile/cell phone)?
• How loud is the desired voice relative to the noise?
• Is the original recording available? If so, what type of media is it on?
• Is there a digital copy that could be emailed for an informal evaluation?
  

Leaving aside the questions regarding legal matters, what I try to find out is how good the recording is (i.e. bandwidth, dynamic range, wow-and-flutter, etc.), how much noise will have to be removed to hear most or all of the words, and, after the noise is taken away, will there be enough speech left to understand.

There is no way to avoid the uncertainty due to differences in terminology, technical savvy, and the like, but going through this question and answer process usually does let me give them some useful feedback and some confidence in whether it is likely worthwhile to proceed or not.