Again, as was said above, if the data is mission-critical, take it to a Recovery Specialist. They have resources and tools that we regular techs can't hope to maintain (like Clean Rooms.)
If it is important data, but not mission-critical, then I would start with a backup from a Linux LiveCD, using dd-rescue, to another 1TB drive, and then start the recovery with testdisk. This way, if the data you are looking for still isn't recovered, you still have the original disk and the option to take it to a Recovery Specialist.
If the data is "important" as in your daughter's pictures from her trip with the Girl Guides, and you don't want to hear her sobbing and pleading, then perhaps you can run something like Lexar's Recovery utility on the drive. Anything that the utility recognizes as having been even a part of an image will get recovered.
And, now the word of warning: If the external was a LaCie, stop using it! I have had more than enough issues with their externals, both professionally and personally to not trust them even for scratch space anymore. Just my 2 cents.