Make the simple syrup. If you don't already have some on hand: combine 1/2 cup sugar and 1/2 cup water in a small saucepan, bring to a simmer, stir until the sugar is fully dissolved, and let cool. That's it. Store any extra in the fridge; it keeps for weeks.

Juice the citrus. Roll the limes and oranges firmly on the counter before juicing; it breaks down the membranes and gets you more juice. For one or two limes or lemons, a handheld citrus juicer (the kind that looks like giant pliers) is fine. For this volume of citrus, see the note below about the manual press. Strain out the seeds and most of the pulp either way.

Combine. Mix the lime juice, orange juice, and simple syrup together. Stir well or shake in a sealed jar.

Store. Keep in the fridge in a sealed jar or pitcher for up to two weeks. For longer storage, freeze. The mix will not freeze hard because of the sugar content; it will be slushy and scoopable, which is actually convenient.