On rainy days buckets would need to be put out to catch water dripping from the ceiling. In the past, I would call a roofer and get out a pile of cash. During one of those wallet thinning meetings with a roofer, he explained to me that often the valleys of the roof is where the leak is coming from. Roofs will be built with the tiles touching each other in the valley causing leaves and dirt to build up blocking the water from running down the valley. The build up can get so bad that the water will flow sideways past the flashing, break down the tar paper, and leak through the roof. It can get so bad that the wood sheathing can rot away (has happened to me, time to call the roofer).
Tracing the new leak up the wall and into the attic, I could see the leak was at a valley. I got on the roof (20 foot high, so took things slow), and did my best to clean out the junk that had built up in the crack of the valley. But there was little room between the tiles to work in, and while cleaning helped, the leak continued. So I put together a few tools, and spent an afternoon on the roof cutting open the valley to look like I have seen done by roofers.
Below is what it looked like working up the valley. The left has enough of the tile cut back to open a channel for the water to flow down the flashing in the valley. The right side shows progress working through the layers of tile and the 4 1/2 in diamond saw used to cut the concrete tile.
It was slow going, marking where to cut, shimming under the tiles to protect the flashing, cutting tiles, and chipping out the part to be removed. But since clearing a gap between the tiles, the rain rushes out and the leaking through the roof has stopped.
This is not a good project for the new DIYer. Working on a sloped roof can be very dangerous and mistakes can damage a roof requiring expensive repairs. But I was able to spend a few hours on my roof and stop a leak for very little money. For tools I used a cheap angle grinder, a diamond cutting wheel (less then $20), a wide ruler and white grease pencil to mark the cut lines, ear protection, dust mask, eye glasses, gloves, and a pick to shim up the tiles and chip out the cut tiles.