dog-end 
noun British informal
1A cigarette end.Put up litter bins and ash trays for their dog-ends and it just legitimises it more from an acceptability stance....
- I stirred it with my foot then stubbed out the dog-end on the linoleum.
- I wandered despondently along, trailing my new sports bag through the dog-ends and sweet wrappers that littered the concrete of the playground.
1.1The last and least pleasing part of something: the dog-end of a hard day...
- The cartoonists portray the dog-end days of December as Old Man Time, complete with scythe, calling the year to its doom.
- Budget 2004 was one the government could have done without: an obligatory address in the dog-end of a parliament.
- It's December at the dog-end of the last century and Liam slouches on a sofa in a Santa Monica hotel, curling his bottom lip and affecting disinterest.