Learn English – How to express pouring to the very top of a receptacle

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For different types of receptacles, such as glasses, cups, jars, pots etc., what is a natural way to describe pouring until its volume is full of the liquid?

A construct pour up comes to my mind, but not sure whether it is correct. I also didn't find any support in dictionaries. Example sentence:

The waiter poured my glass up.

Best Answer

fill to the brim, as defined by The Free Dictionary:

filled all the way full; filled up to the top edge.

I like my coffee cup filled to the brim.
If the glass is filled to the brim, I can't drink without spilling the contents.

Your example can be rephrased as:

The waiter filled my glass to the brim.

A bit flowery, but it gets the job done.