diff --git a/pyomo/solvers/plugins/solvers/gurobi_direct.py b/pyomo/solvers/plugins/solvers/gurobi_direct.py
index ed66a4e0e7b..9cd81ba8a55 100644
--- a/pyomo/solvers/plugins/solvers/gurobi_direct.py
+++ b/pyomo/solvers/plugins/solvers/gurobi_direct.py
@@ -32,7 +32,6 @@
 from pyomo.opt.results.solver import TerminationCondition, SolverStatus
 from pyomo.opt.base import SolverFactory
 from pyomo.core.base.suffix import Suffix
-import pyomo.core.base.var
 
 
 logger = logging.getLogger('pyomo.solvers')
@@ -308,7 +307,7 @@ def _get_expr_from_pyomo_repn(self, repn, max_degree=2):
 
         new_expr += repn.constant
 
-        return new_expr, referenced_vars
+        return new_expr, referenced_vars, degree
 
     def _get_expr_from_pyomo_expr(self, expr, max_degree=2):
         if max_degree == 2:
@@ -317,7 +316,7 @@ def _get_expr_from_pyomo_expr(self, expr, max_degree=2):
             repn = generate_standard_repn(expr, quadratic=False)
 
         try:
-            gurobi_expr, referenced_vars = self._get_expr_from_pyomo_repn(
+            gurobi_expr, referenced_vars, degree = self._get_expr_from_pyomo_repn(
                 repn, max_degree
             )
         except DegreeError as e:
@@ -325,7 +324,7 @@ def _get_expr_from_pyomo_expr(self, expr, max_degree=2):
             msg += '\nexpr: {0}'.format(expr)
             raise DegreeError(msg)
 
-        return gurobi_expr, referenced_vars
+        return gurobi_expr, referenced_vars, degree
 
     def _gurobi_lb_ub_from_var(self, var):
         if var.is_fixed():
@@ -404,10 +403,12 @@ def _create_model(self, model):
         self._init_env()
         if self._solver_model is not None:
             self._solver_model.close()
-        if model.name is not None:
-            self._solver_model = gurobipy.Model(model.name, env=self._env)
-        else:
-            self._solver_model = gurobipy.Model(env=self._env)
+
+        self._solver_model = (
+            gurobipy.Model(model.name, env=self._env)
+            if model.name is not None
+            else gurobipy.Model(env=self._env)
+        )
 
     def close(self):
         """Frees local Gurobi resources used by this solver instance.
@@ -489,6 +490,13 @@ def _set_instance(self, model, kwds={}):
     def _add_block(self, block):
         DirectOrPersistentSolver._add_block(self, block)
 
+    def _addConstr(self, degree, lhs, sense=None, rhs=None, name=""):
+        if degree == 2:
+            con = self._solver_model.addQConstr(lhs, sense, rhs, name)
+        else:
+            con = self._solver_model.addLConstr(lhs, sense, rhs, name)
+        return con
+
     def _add_constraint(self, con):
         if not con.active:
             return None
@@ -499,15 +507,11 @@ def _add_constraint(self, con):
         conname = self._symbol_map.getSymbol(con, self._labeler)
 
         if con._linear_canonical_form:
-            gurobi_expr, referenced_vars = self._get_expr_from_pyomo_repn(
+            gurobi_expr, referenced_vars, degree = self._get_expr_from_pyomo_repn(
                 con.canonical_form(), self._max_constraint_degree
             )
-        # elif isinstance(con, LinearCanonicalRepn):
-        #    gurobi_expr, referenced_vars = self._get_expr_from_pyomo_repn(
-        #        con,
-        #        self._max_constraint_degree)
         else:
-            gurobi_expr, referenced_vars = self._get_expr_from_pyomo_expr(
+            gurobi_expr, referenced_vars, degree = self._get_expr_from_pyomo_expr(
                 con.body, self._max_constraint_degree
             )
 
@@ -523,7 +527,8 @@ def _add_constraint(self, con):
                 )
 
         if con.equality:
-            gurobipy_con = self._solver_model.addConstr(
+            gurobipy_con = self._addConstr(
+                degree=degree,
                 lhs=gurobi_expr,
                 sense=gurobipy.GRB.EQUAL,
                 rhs=value(con.lower),
@@ -535,14 +540,16 @@ def _add_constraint(self, con):
             )
             self._range_constraints.add(con)
         elif con.has_lb():
-            gurobipy_con = self._solver_model.addConstr(
+            gurobipy_con = self._addConstr(
+                degree=degree,
                 lhs=gurobi_expr,
                 sense=gurobipy.GRB.GREATER_EQUAL,
                 rhs=value(con.lower),
                 name=conname,
             )
         elif con.has_ub():
-            gurobipy_con = self._solver_model.addConstr(
+            gurobipy_con = self._addConstr(
+                degree=degree,
                 lhs=gurobi_expr,
                 sense=gurobipy.GRB.LESS_EQUAL,
                 rhs=value(con.upper),
@@ -636,7 +643,7 @@ def _set_objective(self, obj):
         else:
             raise ValueError('Objective sense is not recognized: {0}'.format(obj.sense))
 
-        gurobi_expr, referenced_vars = self._get_expr_from_pyomo_expr(
+        gurobi_expr, referenced_vars, degree = self._get_expr_from_pyomo_expr(
             obj.expr, self._max_obj_degree
         )
 
diff --git a/pyomo/solvers/plugins/solvers/gurobi_persistent.py b/pyomo/solvers/plugins/solvers/gurobi_persistent.py
index 94a2ac6b734..447d1de9b40 100644
--- a/pyomo/solvers/plugins/solvers/gurobi_persistent.py
+++ b/pyomo/solvers/plugins/solvers/gurobi_persistent.py
@@ -578,7 +578,7 @@ def cbCut(self, con):
         if is_fixed(con.body):
             raise ValueError('cbCut expected a non-trivial constraint')
 
-        gurobi_expr, referenced_vars = self._get_expr_from_pyomo_expr(
+        gurobi_expr, referenced_vars, degree = self._get_expr_from_pyomo_expr(
             con.body, self._max_constraint_degree
         )
 
@@ -656,7 +656,7 @@ def cbLazy(self, con):
         if is_fixed(con.body):
             raise ValueError('cbLazy expected a non-trivial constraint')
 
-        gurobi_expr, referenced_vars = self._get_expr_from_pyomo_expr(
+        gurobi_expr, referenced_vars, degree = self._get_expr_from_pyomo_expr(
             con.body, self._max_constraint_degree
         )