Roy:
and for Azure.
Most image manipulation tools feature a 'layers' facility. All i did was first made a new clean background, just with a few colours picked from the original. In fact i painted over the whole of the original picture using broad unfussy strokes with a big brush. Then i gave it a heavy dose of gaussian blur, and that was the basic background. Then i went to 'layers' and clicked on 'import from file', and loaded the original file on top of the new background. Then, with the eraser tool i rubbed out all of the old cluttered background, (but leaving the Blackcap), and revealing the new one beneath.
It is hard to achieve a really smooth gradation for a background when trying this, and if you try to run the noise reduction on top of it you get all sorts of crazy blotches, and swirls. So only run your noise reduction on the bird. While you do gain a nicer looking bokeh, it is hard to retain any small hairs around the bill and chin. Yes Rich, i think the other branch could be left in, just a matter of choice. I haven't got Paintshop, this was done using Paint.NET, a free download, that has loads of tutorial backup, and numerous plug-ins. I recommend it.
PS This was going to the bin anyway. It's always best to get the right shot in the first place, but not always possible.