You can change your API to include additional parameters to limit the scope of data returned by your application.
For instance, you could add limit
and offset
parameters to fetch just a little part. This is how pagination can be done in accordance with REST. A request like this would result in fetching 10 resources from the messages collection, from 21st to 30th. This way you can ask for a specific portion of a huge data set:
myapi.co.uk/messages?limit=10&offset=20
Another way to decrease the payload would be to only ask for certain parts of your resources' representation. Here's how facebook does it:
/joe.smith/friends?fields=id,name,picture
Remember that while using either of these methods, you have to provide a way for the client to discover each of the resources. You can't assume they'll just look at the parameters and start changing them in search of data. That would be a violation of the REST paradigm. Provide them with the necessary hyperlinks to avoid it.
I strongly recommend viewing this presentation on RESTful API design by apigee (the screencast is called "Teach a Dog to REST"). Good practices and neat ideas to approach everyday problems are discussed there.
EDIT: The video has been updated a number of times since I posted this answer, you can check out the 3rd edition from January 2013
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