If you are rightly concerned about chucking expensive absinthe down the drain then consider straining into a shot glass and serve on the side. The roughly...
A very smooth version. I’m in the minimal absinthe camp (can’t abide licorice), so I eschewed the shot. I believe Jerry Thomas’ term for putting fine ice in a glass to chill it was to frappe (frapp-ay) it, so I rinsed and frappayed, threw and strained. Then I smiled.