Making a table sortable with jQuery sortable

I’m trying to replicate a sortable list like in an iPhone / iPad app. In iOS, they have a graphic of three grey lines to signify the ability to sort the table.

I’ve been able to get a table to be sortable using jQuery sortable and even found a small plugin to make it work perfectly inside iOS. My problem is that the whole row is able to be grabbed and sorted. I need to alter it so that only the table cell containing the sortable image is able to be grabbed.

Here is what I have so far:

I was able to get sortable working on iOS from this: