The music veteran, who joined the band in 1979, died in London last Friday (04Sep15) at the age of 80, and his death has now been mourned by founding member Dammers.
In a statement, Dammers thanks Rodriguez for his contribution to The Specials and credits him with improving their music.
He says, "It's hard to express how sad I feel about the death of Rico Rodriguez. He taught me so much about what a proper musician is supposed to try and do. For me, getting to play with him was one of the greatest things about The Specials. His album Man from Wareika had been one of my all-time favourites and a great inspiration.
"I could not believe that he had agreed to play with us, and his contribution to The Specials was immeasurable. He provided an all-important link to authentic Jamaican ska and reggae, which we had tried to copy, and his trombone added the essential element which took us to a next level and helped offer the band a possibility of progression beyond the confines of punk."