Rejected E-3 and Visa Waiver Program

[pbhogineni]

All, I am an australian citizen and have travelled to US on Visa Waiver Program in 2010 for 50 days. Later I have a E-3 visa rejection in the 2011 under 221(g) query (think this relates to the employer). But the same is not reflected on my passport, I mean I do not see any rejection stamp.

Jan of this year I wanted to visit my sister living in the US. Got the visa waiver approval and flew in to DC. But I was denied entry/deported by customs saying that I need a valid visa to enter US and have inappropriately filled the visa waiver application.

Last month I got a 2 year contract opportunity with a IT services company in Chicago. So would like to get advice on how to proceed now. Following are the questions I have. Please advice. Any suggestions are greatly appreciated.

1) Should I opt for E-3 or H1-B? (Note: I do not have intent of staying in US permanently)

2) What are my chances of approval if I apply for an E-3.

3) Will I be denied since I was deported earlier?

Regards

[JoeF]

The H1 quota is full...