Siemsen surname

My ggrandfather Charles William (Carl Wilhelm) SIEMSEN immigrated to St. Louis, MO abt 1850 from Denmark.According to 1870 Census, Holstein, was listed as birthplace and on 1880 census, Denmark was used as birthplace.He was born abt 1819.There were other Siemsens who immigrated at about the same time: Theodore, Peter, George, Theodor and Nicholas.None of the documents that I have found have the village or town in Denmark.I do not know were to begin searching for birth records.Any help or direction will be most appreciated.