Remake, reuse or recyle from "old gold"
I love to suggest clean designs that combine a structure of properly balanced gold with accents made from your old gold (improved alloy). Of course I can also send your jewellery to the refinery where they recycle the gold into pure properly balanced 24k gold, then sells it back to us as fine gold, ready to be alloyed and made into new pieces.

Melting different pieces of old gold together in one crucible, may create an alloy that is unpredictable and inherently unstable.
Reusing “old gold” by melting it to create a new piece is often problematic. The gold melted down from old pieces does not have the same properties as a new alloy. This can reach from problems when milling and working the material, over visible irregularities (and even holes) in the new piece, to worst case: the material becoming brittle and porous with time until it will break.
It is completely understandable that you may want to reuse a piece of jewellery due to sentimental reasons, especially if the gold jewellery has been handed down through your family in this case you need to be aware that there are risks and limitations as to what can actually be created from a melted down piece of jewellery.
Alloys
Every carat gold alloy is created for a specific use. Manufacturers treat them as trade secrets and even have them patented.
The percentage of gold is legally determined, but the alloy metals can be very different, all depending on the intended use of the piece. Alloys designed for rolling or stamping will be very different than for gold used for casting. The latter is often alloyed with zink and sometimes even traces of silicone to improve the flow characteristics.
Colour
The metals added to the gold will determine its colour. White gold is achieved with silver, manganese or palladium additions, while yellow and red golds are alloyed mostly with copper and silver.
Melting pieces of red and yellow gold is likely to result in a "dirty" shade of red gold and
The process of melting the gold and milling it to a fresh sheet or wire changes a gold alloy, eg. some additions (such as zinc) boil off as vapor when the gold is melted.
Impurities
Solder joints have an additional impact on the gold's property, so have repairs and not to forget the use of the gold object over the years will equally introduce impurities into the gold jewelry.

How to properly reuse old gold?
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Create a fresh alloy form just one old piece with fine gold. A healthy approach would be to use only one old piece of low carat (eg. 8 or 14 carat) and top with fine gold to make an improved alloy of 18 carat to avoid working with new additives in the alloy.
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If you insist on melting down two or more pieces, I'll reduce the risk by adding at least the same amount of fine gold and add only add one metal (silver) to create an improved alloy.
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If the old piece contains many joints the old solder will decrease the properties of the new alloy. The design needs to be adapted accordingly.
Last but not least:
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Making a mixed alloy from gold of different carat levels and colours is never (never ever) a good idea.