We have been breeding and showing miniature dachshunds for over 30 years with a primary interest in the smooth coat venturing into the wire and long coats later.  With the longhair coats came a new coat color to us, the cream.  We heard terms like: American cream, English cream, shaded cream, black and cream, brindled creams, etc.  There was not a lot of agreement regarding the genetics of the cream color.  While I am not a geneticist, I am a retired fisheries research biologist with a reasonably good understanding of basic genetics.  While many coat colors were reasonably well understood, some were not.  Development of new genetic testing methods verified most of the color genetics, but the genetics of the cream coat color involved much speculation.

The following are some genetic terms used in this article:
    1) Alleles- these are genes in pairs (one from each parent) with the dominant gene shown in capital letters and the recessive gene in lower case.
    2) Locus- genes and locus are used interchangeably.
    3) Dominant and recessive genes- The presence of one dominant gene in a locus dictates the color or pattern, while It takes two recessive genes at a locus to express the same color or pattern.
    4) Phenotype/genotype- The genotype is the actual genetic makeup of the allele, such as EE, Ee or ee, while the phenotype is what color or pattern is actually expressed in the coat.

I believe that there are four genetic possibilities for the cream coat color: 1) the dilute red in which the basic red color is diluted by the double recessive allele located on the D locus; 2) the red coat color may be modified the the E-locus via the double recessive allele: 3) the possible presence of a chinchilla allele on the C-locus, which should be the double recessive gene which dilutes the red color: and 4) the possible existence of a gene on the I-locus controlling the intensity of the red color and probably is a double recessive.  While there are no known genetic tests for the chinchilla genes or the intensity gene, there were tests for the dilute and extension gene.  Neither of these genes appear to fully explain the cream coat color.
Four Possible Genetic Combinations for Cream Colored Coats in Dachshunds.
    1- Cream color with some black hair with black nose leather and toenails.
            The A-alelle is either AyAy (red) or Ayat (red carrying black and tan), D-allele dominant expressed     as DD or Dd, the E or Extension allele is either EE or Ee and the I-allele is double recessive (ii).  This     could include either cream or shaded cream.

    2- This cream colored coat would have no black hairs with red or light whiskers.
        The A-allele would be the same as above, the D-allele would be the same as above, the I- allele would     also be the same as in No. 1.  This could explain the clear cream coat with no black hairs including the     whiskers.

    3- This cream colored coat would have a bluish nose leather and toenails.  
        The red coat color genetics would be the same as found in 1 and 2, but the D-allele (dilute) would be          double recessive (dd).  Likely this dog could have alopecia issues.

    4- Some breeders believe that the English Cream is caused by the presence of two recessive genes     found on the C-allele called chinchilla (chch).  
        The existence of this chch allele has yet to be found by geneticists, in fact studies of the C-allele          suggest that there are no verifiable mutations on this locus except for albinism which is recessive to         the dominant C gene which allow normal color production.