In　this　paper,　we　study　the　estimation　for　a　partial-linear　single-index　model.　A　two-stage　estimation　procedure　is　proposed　to　estimate　the　link　function　for　the　single　index　and　the　parameters　in　the　single　index,　as　well　as　the　parameters　in　the　linear　component　of　the　model.　Asymptotic　normality　is　established　for　both　parametric　components.　For　the　index,　a　constrained　estimating　equation　leads　to　an　asymptotically　more　efficient　estimator　than　existing　estimators　in　the　sense　that　it　is　of　a　smaller　limiting　variance.　The　estimator　of　the　nonparametric　link　function　achieves　optimal　convergence　rates,　and　the　structural　error　variance　is　obtained.　In　addition,　the　results　facilitate　the　construction　of　confidence　regions　and　hypothesis　testing　for　the　unknown　parameters.　A　simulation　study　is　performed　and　an　application　to　a　real　dataset　is　illustrated.　The　extension　to　multiple　indices　is　briefly　sketched.