Punctuating compound subordinate clauses

How would I punctuate this compound subordinate clause? Other than the "As soon as" at the beginning of the clause, the rest of the clause appears as a compound sentence, which would normally imply that a comma would be necessary to split the two independent-appearing parts of the dependent clause (after "closed"). But a comma would follow the clause, before the true independent part of the sentence. Do I put a comma in the midst of the two parts of the subordinate clause?

"As soon as the door closed and I had settled into my La-Z-Boy. . . ."