Place watermelon, cucumber and agave into base of cocktail shaker.
Muddle watermelon and cucumber, it will turn into mostly juice quite quickly, then mash the stray whole pieces of watermelon and cucumber as best you can.
Add tequila and lime, then add ice until the shaker is almost full.
Cover shaker and shake vigorously.
Remove cover of shaker, then place cocktail strainer on top of the shaker.
Pour cocktail into martini glass through the fine strainer (you are straining the cocktail twice at the same time)
To garnish, cut a diagonal slit into the peel and white flesh of the watermelon slice, then cut away some of the watermelon flesh so that it does not fall off the glass.
Place watermelon garnish on edge of glass and serve immediately.