Saul, Saul, which was it?

I mentioned the contradictions in Paul's conversion stories here, but it seems that there is yet another major contradiction that either calls Galatians or Acts into question.

In Galatians, a largely undisputed epistle of Paul, he says that he did not straight away go to Jerusalem to see the other Apostles after his conversion.

But when he who had set me apart before I was born, and had called me through his grace, was pleased to reveal his Son to me, in order that I might preach him among the Gentiles, I did not confer with flesh and blood, nor did I go up to Jerusalem to those who were apostles before me, but I went away into Arabia; and again I returned to Damascus. Then after three years I went up to Jerusalem to visit Cephas, and remained with him fifteen days. But I saw none of the other apostles except James the Lord's brother. (In what I am writing to you, before God, I do not lie!) (Galatians 1:15-20 RSV)

But then the account in Acts say the exact opposite. After he left Damascus the first time he went straight to Jerusalem and eventually mixed freely with the Apostles.

And when he had come to Jerusalem he attempted to join the disciples; and they were all afraid of him, for they did not believe that he was a disciple. But Barnabas took him, and brought him to the apostles, and declared to them how on the road he had seen the Lord, who spoke to him, and how at Damascus he had preached boldly in the name of Jesus. So he went in and out among them at Jerusalem, (Acts 9:26-28 RSV)

This contradiction matters as Paul is making a serious point in Galatians which testifies to his right to claim Apostleship. Paul claims to have been called directly by God. His Apostleship was not given by other Apostles and he did not confer with them. If the Acts account is true then Paul's argument here in Galatians is undermined. He even goes so far to assure us that he isn't lying.