The day I made Major Tom Mild and Capt. Hastings Bitter I received not one, but two stuck mashes.  In using the perforated screen (below left), I'd always had a little chunkiness when I was recirculating the mash.  At the end of the brew day I would notice that most of the time there was a little bit of mash that would get under the screen.  It never sat quite right on the bottom of the tun.  If I worked at it, I could probably get it to fit more ideally.

After my first stuck mash that day, I tweaked the copper pipe inside the tun.  I felt confident that the next mash would go perfectly.  When it didn't, I knew that next time I would mash with the Bazooka T screen that has been in my HLT.  When I assembled my rig a few years ago, I wanted to be able to switch all 3 tuns around for various brewing situations.  That's why one has a T, another a perforated false bottom, and the third has a copper pipe leading to a stainless steel scrubby for a screen.  When I made the Wigan beer I used the T for mashing and all went perfectly and efficiency didn't suffer.  It was the quickest brew day (4 hours) that I think I've ever had.