This paper investigates the ease with which recent immigrants to Australia from different countries and with different visa categories enter employment at an appropriate level to their prior education and experience in the source country. Unlike most of the earlier research in this field that studied the labour market status of migrants (probabilities of employment, or unemployment, or participation, or wage equation) this paper focuses on the quality of job that the migrant obtains on arrival in Australia. We provide alternative definitions of what is a good job in terms of objective and subjective criteria. The paper uses two sets of the Longitudinal Survey of Immigrants to Australia data: the first cohort that arrived in 1993-95 and the second cohort that arrived in 1999-2000. In particular we would study how changes in social security legislation in 1997, (two year waiting period for eligibility for benefits) affected the quality of job held by new migrants. In comparing the behaviour of migrants in the labour market with and without access to social security benefits we would study whether migrants are more likely to accept bad jobs after the legislative changes. The paper uses bivariate probit models to estimate the probabilities of holding a good job in terms of the usual human capital and demographic variables (including the visa category for entry into Australia). Our results suggest that the policy change had a positive impact on the probability to find a job but a negative impact to hold a good job.