iPhoto / Aperture/ Photoshop Elements

I have the iPhoto 11/ Aperture/ Photoshop Elements 9 software combination.
When I have exported a photo to Photoshop and edited it there, how do I save it back to the iPhoto / Aperture library?
When I used iPhoto 8 and no Aperture it was easy, just saved to the "modified" event folder in iPhoto. Now, I cannot find that route. Any ideas?

Short version: you've been doing it wrong the whole time.

I know that iPhoto (and Aperture, IIRC) allow you to specify third-party editors in the preferences. The correct procedure is as follows (iPhoto directions, should work the same way in Aperture):

1. Set your preferred third-party editor in iPhoto.
2. Select a picture you want to edit in iPhoto. Right click-on the picture and choose to open it in the third-party editor.
3. The third-party program opens automatically. Perform your edits.
4. When finished, press save.
5. Close the third-party editor if you're completely done with editing.
6. Switch back to iPhoto, and your edited photo is there (and can still be reverted back to the original if you want).

Many thanks Chas. Never knew it was so simple.

Oops! Spoke too soon.
I did what you said Chas.
I opened the photo in the chosen external editor, Photoshop Elements, the RAW preview bit, and did the initial RAW preview edits. Then I tried:
1. Using the save button in PE RAW preview: the edited version did not appear back in iPhoto, and
2. From PE RAW preview I opened the image in PE itself and tried to save from there. Again it did not work.

Any ideas?

My directions were correct for JPG images, but RAW files are often separated into two or more components depending on how they were shot. I'm not sure that the directions I gave work for some types of RAW files. When I have a moment I'll try opening a sample RAW file and see if I can duplicate your results.

Hi Chas. Thanks for looking again.

I have just finished a very long session with Apple Care support (my iMac + software is very new) and they could not solve the problem, in spite of being very painstaking and helpful.

My issues, more clearly expressed are, and remain,

editing Raw via iPhoto
1. I shoot photos in Raw and import to iPhoto (latest version). This library is shared by Aperture.
2. I can export a Raw file to Photoshop Elements 9 (PE9), to their Adobe Camera Raw screen (ACR). There i amend it and save image.
3. The saved image is in PE9 and can be further edited.
4. Then I try to save back to iPhoto. It won't save as a JPEG. I can save as a .psd or .tif etc but not .jpg. And if I save as .psd or .tif, I cannot steer them back into the original iPhoto "event".
5. A workaround was offered. Save as Tiff to desktop or to file in folder on desktop. Then via Preview export as Jpeg. Then import to iPhoto. And use Automater to automate. Not easy. And still need to get the edited images back to the right events (merge perhaps) in iPhoto.

OR

editing Raw via Aperture
1. As before
2. Export to PE9 from Aperture. It will not open the ACR screen so am limited to use of the Raw processing available in Aperture (not as good / convenient etc). I can further edit in PE9 though. But when I try and save, same problems as above i.e. cannot save as Jpeg and need a complex workflow.