diff --git a/pyomo/contrib/piecewise/tests/common_tests.py b/pyomo/contrib/piecewise/tests/common_tests.py
index 14ce6f5ae12..523853ec3c5 100644
--- a/pyomo/contrib/piecewise/tests/common_tests.py
+++ b/pyomo/contrib/piecewise/tests/common_tests.py
@@ -10,7 +10,8 @@
 import pyomo.contrib.piecewise.tests.models as models
 from pyomo.core import Var
 from pyomo.core.base import TransformationFactory
-from pyomo.environ import value
+from pyomo.core.expr.compare import assertExpressionsEqual
+from pyomo.environ import value, Expression
 from pyomo.gdp import Disjunct, Disjunction
 
 
@@ -85,3 +86,25 @@ def check_descend_into_expressions_objective_target(test, transformation, m=None
     test.check_pw_log(m)
     # And check that the paraboloid was *not* transformed.
     test.assertIsNone(m.pw_paraboloid.get_transformation_var(m.paraboloid_expr))
+
+
+def check_single_segment_no_disjunction(test, transformation, m=None):
+    if m is None:
+        m = models.make_single_segment_log_x_model()
+    transform = TransformationFactory(transformation)
+    transform.apply_to(m)
+
+    # A single segment doesn't require making a discrete choice, so this
+    # should not have created any GDP components.
+    test.assertEqual(len(list(m.component_data_objects(Disjunct))), 0)
+    test.assertEqual(len(list(m.component_data_objects(Disjunction))), 0)
+    # Nor should it have introduced any new Vars (such as a substitute_var
+    # or an indicator_var)--m.x should be the only Var in the model.
+    model_vars = list(m.component_data_objects(Var))
+    test.assertEqual(len(model_vars), 1)
+    test.assertIs(model_vars[0], m.x)
+
+    z = m.pw_log.get_transformation_var(m.log_expr)
+    test.assertIsInstance(z, Expression)
+    assertExpressionsEqual(test, z.expr, m.f1(m.x), places=7)
+    test.assertIs(m.log_expr.expr, z)
diff --git a/pyomo/contrib/piecewise/tests/models.py b/pyomo/contrib/piecewise/tests/models.py
index dc96e052c38..7e2efa2728e 100644
--- a/pyomo/contrib/piecewise/tests/models.py
+++ b/pyomo/contrib/piecewise/tests/models.py
@@ -45,7 +45,7 @@ def f3(x):
     m.x1 = Var(bounds=(0, 3))
     m.x2 = Var(bounds=(1, 7))
 
-    ## apprximates paraboloid x1**2 + x2**2
+    ## approximates paraboloid x1**2 + x2**2
     def g1(x1, x2):
         return 3 * x1 + 5 * x2 - 4
 
@@ -72,3 +72,19 @@ def c_rule(m, i):
     m.indexed_c = Constraint([0, 1], rule=c_rule)
 
     return m
+
+
+def make_single_segment_log_x_model():
+    m = ConcreteModel()
+    m.x = Var(bounds=(1, 10))
+    m.pw_log = PiecewiseLinearFunction(points=[1, 10], function=log)
+
+    def f1(x):
+        return (log(10) / 9) * x - log(10) / 9
+
+    m.f1 = f1
+
+    m.log_expr = m.pw_log(m.x)
+    m.obj = Objective(expr=m.log_expr)
+
+    return m
diff --git a/pyomo/contrib/piecewise/tests/test_disaggregated_logarithmic.py b/pyomo/contrib/piecewise/tests/test_disaggregated_logarithmic.py
index 9ffa35fcfb3..575e9c02728 100644
--- a/pyomo/contrib/piecewise/tests/test_disaggregated_logarithmic.py
+++ b/pyomo/contrib/piecewise/tests/test_disaggregated_logarithmic.py
@@ -263,6 +263,11 @@ def test_descend_into_expressions_objective_target(self):
             self, 'contrib.piecewise.disaggregated_logarithmic'
         )
 
+    def test_single_segment_no_disjunction(self):
+        ct.check_single_segment_no_disjunction(
+            self, 'contrib.piecewise.disaggregated_logarithmic'
+        )
+
     # Check solution of the log(x) model
     @unittest.skipUnless(SolverFactory('gurobi').available(), 'Gurobi is not available')
     @unittest.skipUnless(SolverFactory('gurobi').license_is_valid(), 'No license')
diff --git a/pyomo/contrib/piecewise/tests/test_incremental.py b/pyomo/contrib/piecewise/tests/test_incremental.py
index e6e8d659d1f..015cbb02261 100644
--- a/pyomo/contrib/piecewise/tests/test_incremental.py
+++ b/pyomo/contrib/piecewise/tests/test_incremental.py
@@ -174,6 +174,9 @@ def test_descend_into_expressions_objective_target(self):
             make_log_x_model(simplices=self.ordered_simplices),
         )
 
+    def test_single_segment_no_disjunction(self):
+        ct.check_single_segment_no_disjunction(self, 'contrib.piecewise.incremental')
+
     @unittest.skipUnless(SolverFactory('gurobi').available(), 'Gurobi is not available')
     @unittest.skipUnless(SolverFactory('gurobi').license_is_valid(), 'No license')
     def test_solve_log_model(self):
diff --git a/pyomo/contrib/piecewise/tests/test_inner_repn_gdp.py b/pyomo/contrib/piecewise/tests/test_inner_repn_gdp.py
index 57d15dc3398..73b9e997fcf 100644
--- a/pyomo/contrib/piecewise/tests/test_inner_repn_gdp.py
+++ b/pyomo/contrib/piecewise/tests/test_inner_repn_gdp.py
@@ -106,6 +106,9 @@ def test_descend_into_expressions_objective_target(self):
             self, 'contrib.piecewise.inner_repn_gdp'
         )
 
+    def test_single_segment_no_disjunction(self):
+        ct.check_single_segment_no_disjunction(self, 'contrib.piecewise.inner_repn_gdp')
+
     @unittest.skipUnless(SolverFactory('gurobi').available(), 'Gurobi is not available')
     @unittest.skipUnless(SolverFactory('gurobi').license_is_valid(), 'No license')
     def test_solve_disaggregated_convex_combo_model(self):
diff --git a/pyomo/contrib/piecewise/tests/test_nested_inner_repn_gdp.py b/pyomo/contrib/piecewise/tests/test_nested_inner_repn_gdp.py
index b863cb0267b..a867ad3538e 100644
--- a/pyomo/contrib/piecewise/tests/test_nested_inner_repn_gdp.py
+++ b/pyomo/contrib/piecewise/tests/test_nested_inner_repn_gdp.py
@@ -122,6 +122,11 @@ def test_descend_into_expressions_objective_target(self):
             self, 'contrib.piecewise.nested_inner_repn_gdp'
         )
 
+    def test_single_segment_no_disjunction(self):
+        ct.check_single_segment_no_disjunction(
+            self, 'contrib.piecewise.nested_inner_repn_gdp'
+        )
+
     # Check the solution of the log(x) model
     @unittest.skipUnless(SolverFactory('gurobi').available(), 'Gurobi is not available')
     @unittest.skipUnless(SolverFactory('gurobi').license_is_valid(), 'No license')
diff --git a/pyomo/contrib/piecewise/tests/test_outer_repn_gdp.py b/pyomo/contrib/piecewise/tests/test_outer_repn_gdp.py
index 902ec21abc5..d00a01a32c0 100644
--- a/pyomo/contrib/piecewise/tests/test_outer_repn_gdp.py
+++ b/pyomo/contrib/piecewise/tests/test_outer_repn_gdp.py
@@ -178,3 +178,6 @@ def test_solve_multiple_choice_model(self):
         SolverFactory('gurobi').solve(m)
 
         ct.check_log_x_model_soln(self, m)
+
+    def test_single_segment_no_disjunction(self):
+        ct.check_single_segment_no_disjunction(self, 'contrib.piecewise.outer_repn_gdp')
diff --git a/pyomo/contrib/piecewise/tests/test_piecewise_linear_function.py b/pyomo/contrib/piecewise/tests/test_piecewise_linear_function.py
index 5bfc564fbad..117fd186d25 100644
--- a/pyomo/contrib/piecewise/tests/test_piecewise_linear_function.py
+++ b/pyomo/contrib/piecewise/tests/test_piecewise_linear_function.py
@@ -102,6 +102,20 @@ def test_pw_linear_approx_of_ln_x_points(self):
         m.pw = PiecewiseLinearFunction(points=[1, 3, 6, 10], function=m.f)
         self.check_ln_x_approx(m.pw, m.x)
 
+    def test_pw_linear_approx_of_ln_x_single_segment(self):
+        m = self.make_ln_x_model()
+        m.pw = PiecewiseLinearFunction(points=[1, 10], function=m.f)
+
+        self.assertEqual(len(m.pw._simplices), 1)
+        self.assertEqual(len(m.pw._linear_functions), 1)
+        self.assertEqual(m.pw._simplices[0], (0, 1))
+
+        slope = log(10) / 9
+        intercept = -log(10) / 9
+        assertExpressionsEqual(
+            self, m.pw._linear_functions[0](m.x), slope * m.x + intercept, places=7
+        )
+
     def test_pw_linear_approx_of_ln_x_linear_funcs(self):
         m = self.make_ln_x_model()
         m.pw = PiecewiseLinearFunction(
diff --git a/pyomo/contrib/piecewise/tests/test_reduced_inner_repn.py b/pyomo/contrib/piecewise/tests/test_reduced_inner_repn.py
index 670386a4df7..46f13f42871 100644
--- a/pyomo/contrib/piecewise/tests/test_reduced_inner_repn.py
+++ b/pyomo/contrib/piecewise/tests/test_reduced_inner_repn.py
@@ -245,6 +245,11 @@ def test_descend_into_expressions_objective_target(self):
             self, 'contrib.piecewise.reduced_inner_repn_gdp'
         )
 
+    def test_single_segment_no_disjunction(self):
+        ct.check_single_segment_no_disjunction(
+            self, 'contrib.piecewise.reduced_inner_repn_gdp'
+        )
+
     @unittest.skipUnless(SolverFactory('gurobi').available(), 'Gurobi is not available')
     @unittest.skipUnless(SolverFactory('gurobi').license_is_valid(), 'No license')
     def test_solve_convex_combo_model(self):
diff --git a/pyomo/contrib/piecewise/transform/disaggregated_logarithmic.py b/pyomo/contrib/piecewise/transform/disaggregated_logarithmic.py
index 8350051309c..7133caf78b5 100644
--- a/pyomo/contrib/piecewise/transform/disaggregated_logarithmic.py
+++ b/pyomo/contrib/piecewise/transform/disaggregated_logarithmic.py
@@ -44,7 +44,9 @@ class DisaggregatedLogarithmicMIPTransformation(PiecewiseLinearTransformationBas
 
     # Implement to use PiecewiseLinearTransformationBase. This function returns the Var
     # that replaces the transformed piecewise linear expr
-    def _transform_pw_linear_expr(self, pw_expr, pw_linear_func, transformation_block):
+    def _transform_multiple_segment_pw_linear_expr(
+        self, pw_expr, pw_linear_func, transformation_block
+    ):
         # Get a new Block for our transformation in transformation_block.transformed_functions,
         # which is a Block(Any). This is where we will put our new components.
         transBlock = transformation_block.transformed_functions[
diff --git a/pyomo/contrib/piecewise/transform/incremental.py b/pyomo/contrib/piecewise/transform/incremental.py
index fb90b328280..8cca6f53bc3 100644
--- a/pyomo/contrib/piecewise/transform/incremental.py
+++ b/pyomo/contrib/piecewise/transform/incremental.py
@@ -43,7 +43,9 @@ class IncrementalMIPTransformation(PiecewiseLinearTransformationBase):
 
     # Implement to use PiecewiseLinearTransformationBase. This function returns the Var
     # that replaces the transformed piecewise linear expr
-    def _transform_pw_linear_expr(self, pw_expr, pw_linear_func, transformation_block):
+    def _transform_multiple_segment_pw_linear_expr(
+        self, pw_expr, pw_linear_func, transformation_block
+    ):
         if pw_linear_func.triangulation not in (
             Triangulation.OrderedJ1,
             Triangulation.AssumeValid,
diff --git a/pyomo/contrib/piecewise/transform/inner_representation_gdp.py b/pyomo/contrib/piecewise/transform/inner_representation_gdp.py
index a7d365224d7..1e5f93a853d 100644
--- a/pyomo/contrib/piecewise/transform/inner_representation_gdp.py
+++ b/pyomo/contrib/piecewise/transform/inner_representation_gdp.py
@@ -50,7 +50,9 @@ class InnerRepresentationGDPTransformation(PiecewiseLinearTransformationBase):
     CONFIG = PiecewiseLinearTransformationBase.CONFIG()
     _transformation_name = 'pw_linear_inner_repn'
 
-    def _transform_pw_linear_expr(self, pw_expr, pw_linear_func, transformation_block):
+    def _transform_multiple_segment_pw_linear_expr(
+        self, pw_expr, pw_linear_func, transformation_block
+    ):
         transBlock = transformation_block.transformed_functions[
             len(transformation_block.transformed_functions)
         ]
diff --git a/pyomo/contrib/piecewise/transform/nested_inner_repn.py b/pyomo/contrib/piecewise/transform/nested_inner_repn.py
index 3128c8002ef..b4b51a70697 100644
--- a/pyomo/contrib/piecewise/transform/nested_inner_repn.py
+++ b/pyomo/contrib/piecewise/transform/nested_inner_repn.py
@@ -52,7 +52,9 @@ class NestedInnerRepresentationGDPTransformation(PiecewiseLinearTransformationBa
 
     # Implement to use PiecewiseLinearTransformationBase. This function returns the Var
     # that replaces the transformed piecewise linear expr
-    def _transform_pw_linear_expr(self, pw_expr, pw_linear_func, transformation_block):
+    def _transform_multiple_segment_pw_linear_expr(
+        self, pw_expr, pw_linear_func, transformation_block
+    ):
         # Get a new Block() in transformation_block.transformed_functions, which
         # is a Block(Any)
         transBlock = transformation_block.transformed_functions[
diff --git a/pyomo/contrib/piecewise/transform/outer_representation_gdp.py b/pyomo/contrib/piecewise/transform/outer_representation_gdp.py
index 1229ce5993b..1bbad6a28ad 100644
--- a/pyomo/contrib/piecewise/transform/outer_representation_gdp.py
+++ b/pyomo/contrib/piecewise/transform/outer_representation_gdp.py
@@ -50,7 +50,9 @@ class OuterRepresentationGDPTransformation(PiecewiseLinearTransformationBase):
     CONFIG = PiecewiseLinearTransformationBase.CONFIG()
     _transformation_name = 'pw_linear_outer_repn'
 
-    def _transform_pw_linear_expr(self, pw_expr, pw_linear_func, transformation_block):
+    def _transform_multiple_segment_pw_linear_expr(
+        self, pw_expr, pw_linear_func, transformation_block
+    ):
         transBlock = transformation_block.transformed_functions[
             len(transformation_block.transformed_functions)
         ]
diff --git a/pyomo/contrib/piecewise/transform/piecewise_linear_transformation_base.py b/pyomo/contrib/piecewise/transform/piecewise_linear_transformation_base.py
index 080eff5aa79..09d3e8ff9d8 100644
--- a/pyomo/contrib/piecewise/transform/piecewise_linear_transformation_base.py
+++ b/pyomo/contrib/piecewise/transform/piecewise_linear_transformation_base.py
@@ -249,6 +249,33 @@ def _transform_objective(self, objective, descend_into_expressions):
             visitor.walk_expression((o.expr, o, 0))
 
     def _transform_pw_linear_expr(self, pw_expr, pw_linear_func, transformation_block):
+        if len(pw_linear_func._simplices) == 1:
+            return self._transform_single_segment_pw_linear_expr(
+                pw_expr, pw_linear_func, transformation_block
+            )
+        return self._transform_multiple_segment_pw_linear_expr(
+            pw_expr, pw_linear_func, transformation_block
+        )
+
+    def _transform_single_segment_pw_linear_expr(
+        self, pw_expr, pw_linear_func, transformation_block
+    ):
+        # There's no actual choice to make between pieces, so we don't need
+        # any discrete variables: We can just substitute the (single) linear
+        # function directly in place of the PiecewiseLinearExpression.
+        transBlock = transformation_block.transformed_functions[
+            len(transformation_block.transformed_functions)
+        ]
+        linear_func = pw_linear_func._linear_functions[0]
+        transBlock.substitute_expr = Expression(expr=linear_func(*pw_expr.args))
+        pw_linear_func.map_transformation_var(pw_expr, transBlock.substitute_expr)
+
+        return transBlock.substitute_expr
+
+    def _transform_multiple_segment_pw_linear_expr(
+        self, pw_expr, pw_linear_func, transformation_block
+    ):
         raise DeveloperError(
-            "Derived class failed to implement '_transform_pw_linear_expr'"
+            "Derived class failed to implement "
+            "'_transform_multiple_segment_pw_linear_expr'"
         )
diff --git a/pyomo/contrib/piecewise/transform/reduced_inner_representation_gdp.py b/pyomo/contrib/piecewise/transform/reduced_inner_representation_gdp.py
index 3ff3395c9fc..49b8efdc9d9 100644
--- a/pyomo/contrib/piecewise/transform/reduced_inner_representation_gdp.py
+++ b/pyomo/contrib/piecewise/transform/reduced_inner_representation_gdp.py
@@ -52,7 +52,9 @@ class ReducedInnerRepresentationGDPTransformation(PiecewiseLinearTransformationB
     CONFIG = PiecewiseLinearTransformationBase.CONFIG()
     _transformation_name = 'pw_linear_reduced_inner_repn'
 
-    def _transform_pw_linear_expr(self, pw_expr, pw_linear_func, transformation_block):
+    def _transform_multiple_segment_pw_linear_expr(
+        self, pw_expr, pw_linear_func, transformation_block
+    ):
         transBlock = transformation_block.transformed_functions[
             len(transformation_block.transformed_functions)
         ]