Something I have recently switched to, and may take a teensy bit of getting used to, is using old rags instead of your disposable tissues.
If you have any old clothes that are too destroyed to make it to charity, or are doing some upcycling on your clohes the excess fabric can be cut into squares/rectangles and used as reusable clothes. Great for wiping noses and wiping up spills, I also used an old salsa jar and created my rag jar for my bed side table!
The used rags can then be thrown in the washing basket or hand washed in the sink. No more need to throw away all those tissues!