front end - How can I overload autocompletion to work with full contexts?

I would like for the autocomplete feature to search through contexts, for example if I have a symbol named A`B`C`MyFunction, when I type A` and press "cmd + shift + k" it will complete it.

Edit

To be clear, I don't want to have to type the path because it's usually very long, and I don't want to have to type the function name again, even if the path itself gets auto completed. I want the following:

If I have these functions:

Very`Long`Context`For`My`Function1
Very`Long`Context`For`My`Function2
...

I want to be able to type Very` and then press CMD+Shift+k, to get a dropdown menu saying exactly

Very`Long`Context`For`My`Function1
Very`Long`Context`For`My`Function2
...

Answer

This is obsolete in Mathematica 9, which automatically includes contexts in completions.

Undocumented function: use at your own risk, subject to change in future versions, etc....

---

The function you're interested in is FE`FC.

It's been around for a while (here's a Mathematica Journal article that references it, near the end) although it has changed argument structure at least once that I'm aware of.

Anyway, here's the code I currently use to a similar end as what Mike would like. (Most of this is boilerplate from the original definition; the main difference is the use of a new function FE`names.)

(* Nice little hack to have command completion (cmd-k) include contexts *)
Unprotect[FE`FC];
ClearAll[FE`FC]


FE`FC[FE`nameString_, FE`ignoreCase_:False] /; $Notebooks:=
    MathLink`CallFrontEnd[FrontEnd`CompletionsListPacket[
        FE`names[FE`nameString<>"*"], FE`ignoreCase],
        FE`NoResult]

FE`names[FE`str_, FE`ignoreCase_:False] :=
    Join[FE`shortContexts[FE`str], Names[FE`str, IgnoreCase -> FE`ignoreCase]];

FE`shortContexts[FE`patt_]:=

 With[{FE`brettclen = Length[StringSplit[FE`patt, "`"]]},
  Union[StringJoin[
      Riffle[Take[#, Min[FE`brettclen, Length[#]]], "`", {2, -1, 2}]] & /@
    StringSplit[Contexts[FE`patt], "`"]]
  ]

Protect[FE`FC];

The end result is that when I use command completion, I get contexts that match in addition to symbols. This isn't quite the same as Mike's request, since it gives the contexts one at a time:

since otherwise the list can get a bit overwhelming. For example, if you typed Int and then tried to complete to IntegerPart, there's a factor of ten difference:

In[5]:= {Length[Names["Int*"]] + Length[Contexts["Int*"]], 
 Length[Names["Int*`*"]]}

Out[5]= {41, 419}