A grain-cleaning machine for obtaining grains has a desired size which is greater than a lower value and less than or equal to an upper value. The grain-cleaning machine comprises an arrangement of sieves. The arrangement of sieves comprises at least two main sieve levels positioned overlapping each other. Each main sieve level comprises a respective fine sieve followed by a respective grain sieve. At least one lower sieve level comprises a respective lower grain sieve. The at least one lower sieve level being positioned below the main sieve levels. Each fine sieve has a first mesh provided with openings having an opening size which is equal to said lower value, and each grain sieve and each lower grain sieve have a second mesh provided with openings having an opening size which is equal to said upper value.