DUBAI, United Arab Emirates -- Novak Djokovic shook off the rust to beat Cedrik-Marcel Stebe 6-4, 6-2 at the Dubai Tennis Championships Monday in his first match since winning the Australian Open. Sixth-seeded Mardy Fish also had an easy time against Andreas Beck of Germany, winning 6-1, 6-1 to join Djokovic in the second round. The top-ranked Djokovic has not played a match in nearly four weeks and it showed at times. He broke the 72nd-ranked German to go up 1-0 but had to save two break points in the fourth game as he struggled with Stebes return game. Stebe pushed the set to 5-4 and deuce before Djokovic hit his first ace and another good serve which the German returned long. Djokovic had an easier second set, breaking twice. He won the match with his third ace of the match and another serve that Stebe couldnt return. "He definitely played well. I was impressed with his game, especially in the first set," Djokovic said of Stebe, who moved up nearly 300 ranking places in 2011 and took Lleyton Hewitt to four sets at the Australian Open last month. "He was hanging in there. I thought I served well when I needed to," Djokovic continued. "It could have gone a different way really, because he was returning well. He was very aggressive on the baseline. You could feel that even though hes young and doesnt have much experience playing on the big stage, he really didnt care much." Djokovic, going for a fourth consecutive Dubai title, is now 8-0 this year after beating Stebe. He insisted that he was not concerned with matching his exploits in 2011, in which he won three Grand Slams and started the season with a 41-match winning streak. "Well, you know, people talk about that obviously, and Im expecting that. But to be honest, Im not really comparing 2012 with 2011," Djokovic said. "I want to have this positive mindset on the court that is going to kind of keep me away from unnecessary pressure that I already have as No. 1 in the world and as a top player, somebody thats expected to win in most of the matches. "The last year was amazing. Definitely best year of my career. If you ask me if I can repeat it, I dont know. Its going to be very, very hard obviously." A few hours before his match, Djokovic was courtside as his younger brother Marko lost his match to Andrey Golubev of Kazakhstan 6-3, 6-2. The 869th-ranked Djokovic was granted a wild card into the tournament. Djokovic serves as a mentor of sorts for the 20-year-old Marko and said it was hard to see his brother struggling, admitting that can difficult for Marko and his other tennis-playing brother 16-year-old Djordje to always be compared to him. "In the end, he has to face this, I guess, pressure in a way for having Djokovic surname," Djokovic said of Marko. "All over the world where he plays tennis, I guess he has to face this pressure that is not necessary for him at this age. Its his burden, and hes very committed. He wants to succeed in tennis." Fish, meanwhile, broke Beck twice in the first set to lead 4-0. In the second, he broke three times before closing it out in 57 minutes. The American has had a mixed year so far, crashing out in the second round of the Australian Open and losing to 388th-ranked Albano Olivetti in the Marseille quarterfinals last week. He did, however, help the United States rout Switzerland 5-0 in the Davis Cup. "Obviously its nice to get through quickly early in the tournaments, but it gets tough from here on out for sure," Fish said. " Ive never played him (Beck) before. I assume hes played better matches for sure. But these courts suit me very well." Fish, who replaced Andy Roddick as the American No. 1 last year, admitted there is a lot of "responsibility" "that comes with that role and he felt it last week in Marseille. "It certainly is different than my past being the third or fourth or 10th American at times," he said. "The match that I played last week in Marseille bugs you a lot more than it used to because you dont want those guys to have that over you. You dont want those guys to beat you. You dont want to give players and your colleagues the idea that youre vulnerable as well." Fish was not satisfied with a 3-2 start in 2012, but relished his Davis Cup experience. "I havent had the best start to the year individually, but I must say Davis Cup in Switzerland certainly made up for the disappointment in Australia. Theres no doubt about that," he said. "Winning that tie and being a part of that with the guys, with captain (Jim) Courier, certainly doesnt feel like a bad start." Jason Castro Astros Jersey. 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