diff --git a/pyomo/solvers/plugins/solvers/mosek_direct.py b/pyomo/solvers/plugins/solvers/mosek_direct.py
index dc1fa0f43a9..972a82a16fa 100644
--- a/pyomo/solvers/plugins/solvers/mosek_direct.py
+++ b/pyomo/solvers/plugins/solvers/mosek_direct.py
@@ -39,6 +39,7 @@
 
 mosek, mosek_available = attempt_import('mosek')
 
+
 class DegreeError(ValueError):
     pass
 
@@ -566,6 +567,16 @@ def _add_block(self, block):
                                      "support multiple objectives.")
                 self._set_objective(obj)
 
+    def _set_whichsol(self):
+        itr_soltypes = [mosek.problemtype.qo, mosek.problemtype.qcqo,
+                        mosek.problemtype.conic]
+        if (self._solver_model.getnumintvar() >= 1):
+            self._whichsol = mosek.soltype.itg
+        elif (self._solver_model.getprobtype() in itr_soltypes):
+            self._whichsol = mosek.soltype.itr
+        elif (self._solver_model.getprobtype() == mosek.problemtype.lo):
+            self._whichsol = mosek.soltype.bas
+
     def _postsolve(self):
 
         extract_duals = False
@@ -589,19 +600,15 @@ def _postsolve(self):
 
         msk_task = self._solver_model
 
-        itr_soltypes = [mosek.problemtype.qo, mosek.problemtype.qcqo,
-                        mosek.problemtype.conic]
+        self._set_whichsol()
 
-        if (msk_task.getnumintvar() >= 1):
-            self._whichsol = mosek.soltype.itg
+        if (self._whichsol == mosek.soltype.itg):
             if extract_reduced_costs:
                 logger.warning("Cannot get reduced costs for MIP.")
             if extract_duals:
                 logger.warning("Cannot get duals for MIP.")
             extract_reduced_costs = False
             extract_duals = False
-        elif (msk_task.getprobtype() in itr_soltypes):
-            self._whichsol = mosek.soltype.itr
 
         whichsol = self._whichsol
         sol_status = msk_task.getsolsta(whichsol)
@@ -975,11 +982,15 @@ def warm_start_capable(self):
         return True
 
     def _warm_start(self):
+        self._set_whichsol()
         for pyomo_var, mosek_var in self._pyomo_var_to_solver_var_map.items():
             if pyomo_var.value is not None:
-                for solType in mosek.soltype.values:
-                    self._solver_model.putxxslice(
-                        solType, mosek_var, mosek_var + 1, [(pyomo_var.value)])
+                self._solver_model.putxxslice(
+                    self._whichsol, mosek_var, mosek_var + 1, [(pyomo_var.value)])
+
+        if (self._version[0] > 9) & (self._whichsol == mosek.soltype.itg):
+            self._solver_model.putintparam(
+                mosek.iparam.mio_construct_sol, mosek.onoffkey.on)
 
     def _load_vars(self, vars_to_load=None):
         var_map = self._pyomo_var_to_solver_var_map