A method for producing a package with an inner volume of the package containing a headspace volume and a volume taken by the product, and a packaging machine. To allow the reduction of the size of such a package, the package is formed providing a product to be packaged inside the package; providing a tray with its height being smaller than the maximum height of the product; placing the product into the tray; replacing the atmosphere surrounding the product by a gas mixture of carbon monoxide, carbon dioxide, and nitrogen; covering the tray containing the product by a formable sheet material; forming the formable sheet material and sealing tray together with the formable sheet material, so that the headspace volume containing the gas mixture makes at most half of the volume taken by the product inside the package.