Removing nested paragraph tags

I'm trying to remove any nested paragraph tags from a huge file. I have come up with the following regex so far...

s/<paragraph>(.*?)<paragraph>(.*?)<\/paragraph>(.*?)<\/paragraph>/<paragraph>$1$2$3<\/paragraph>/ig;

This appears to work in many cases however it also removes every other pair of properly formatted paragraph tags...

e.g.

If the input was the following:

<paragraph>some data</paragraph><paragraph>more data</paragraph><paragraph>even more data</paragraph>

The regex would result in this being changed to:

<paragraph>some data</paragraph>more data<paragraph>even more data</paragraph>

After thinking about it, it makes sense since I am trying to match to four tag units within the text and the (.*?) doesn't exclude other paragraph tags from being included...

Is there anyway to exclude <paragraph> from the (.*?) match?

Thanks...

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