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We consider the problem of model selection and estimation in sparse highdimensional linear regression models with strongly correlated variables. First,we study the theoretical properties of the dual Lasso solution, and we showthat joint consideration of the Lasso primal and its dual solutions are usefulfor selecting correlated active variables. Second, we argue that correlationsamong active predictors are not problematic, and we derive a new weakercondition on the design matrix, called Pseudo Irrepresentable Condition (PIC).Third, we present a new variable selection procedure, Dual Lasso Selector, andwe prove that the PIC is a necessary and sufficient condition for consistentvariable selection for the proposed method. Finally, by combining the dualLasso selector further with the Ridge estimation even better predictionperformance is achieved. We call the combination (DLSelect+Ridge), it can beviewed as a new combined approach for inference in high-dimensional regressionmodels with correlated variables. We illustrate DLSelect+Ridge method andcompare it with popular existing methods in terms of variable selection,prediction accuracy, estimation accuracy and computation speed by consideringvarious simulated and real data examples.