Strange pimpl problem - const correctness not respected by compiler

(I accidentally posted a first version to m.p.dotnet.languages.vc)

Hello!

I have a strange problem with my pimpl implementation. What happens is that
const correctness is not respected by the compiler. Among two methods, one
const and one non-const, the non-const version ends up being called on a
const
object. Let me go straight to the code:

#include <iostream>

struct Geometry {};

class LineData
{
   class LineDataImpl;
   LineDataImpl& mImpl;

public:

   LineData();

   const Geometry& GetGeometry() const;
   /* */ Geometry& GetGeometry() /* */;
};

class LineData::LineDataImpl
{
   Geometry mGeometry;

public:

   const Geometry& GetGeometry() const
   {
      std::cout << "Calling const overload" << std::endl;
      return mGeometry;
   }

   Geometry& GetGeometry()
   {
      std::cout << "Calling non-const overload" << std::endl;
      return mGeometry;
   }
};

LineData::LineData()
   : mImpl(*(new LineDataImpl))
{ }

const Geometry& LineData::GetGeometry() const
{
   return mImpl.GetGeometry();
}

Geometry& LineData::GetGeometry()
{
   return mImpl.GetGeometry();
}

int main()
{
   const LineData lineData;
   const Geometry& geometry = lineData.GetGeometry();

   return 0;
}

This sample shows that despite my intentions of being const correct, the
compiler ends up calling the non-const overload. What is going on here?
I'm using Visual Studio 2008, SP1.

Thanks in advance!

--
Daniel Lidstr?m