diff --git a/mathics/builtin/list/constructing.py b/mathics/builtin/list/constructing.py
index bb6212e5f..c9b84c6c3 100644
--- a/mathics/builtin/list/constructing.py
+++ b/mathics/builtin/list/constructing.py
@@ -566,12 +566,16 @@ class Table(IterationFunction):
     summary_text = "make a table of values of an expression"
 
     def get_result(self, elements, is_uniform=False) -> ListExpression:
-        return ListExpression(
-            *elements,
-            elements_properties=ElementsProperties(
-                elements_fully_evaluated=True, is_uniform=is_uniform
-            ),
-        )
+        # The elements have just been evaluated, but that does not make them
+        # "fully evaluated": that would keep the list from ever being evaluated
+        # again, so that in
+        #   l = Table[x, {1}]; x = 1; l
+        # l would stay {x}. Only a list of literal elements, like a list of
+        # numbers, is fully evaluated, and that is settled here, at creation.
+        result = ListExpression(*elements)
+        if result.is_literal:
+            result._build_elements_properties()
+        return result
 
 
 class Tuples(Builtin):
diff --git a/mathics/core/expression.py b/mathics/core/expression.py
index cd7b54e7d..d9417dcb9 100644
--- a/mathics/core/expression.py
+++ b/mathics/core/expression.py
@@ -436,9 +436,13 @@ def _build_elements_properties(self):
                     element._build_elements_properties()
 
                 # and now possibly adjust self.elements_properties.elements_fully_evaluted
+                # A literal element (e.g. {}, which Map over an empty list
+                # gives with pessimistic properties) is fully evaluated
+                # whatever its own properties say.
                 if self.elements_properties.elements_fully_evaluated:
                     self.elements_properties.elements_fully_evaluated = (
-                        element.elements_properties.elements_fully_evaluated
+                        element.is_literal
+                        or element.elements_properties.elements_fully_evaluated
                     )
 
             if element.is_literal:
@@ -2149,7 +2153,8 @@ def convert_expression_elements(
 
             if elements_properties.elements_fully_evaluated:
                 elements_properties.elements_fully_evaluated = (
-                    converted_elt.elements_properties.elements_fully_evaluated
+                    converted_elt.is_literal
+                    or converted_elt.elements_properties.elements_fully_evaluated
                 )
 
         if elements_properties.is_ordered and last_converted_elt is not None:
diff --git a/test/builtin/list/test_constructing.py b/test/builtin/list/test_constructing.py
index 22159b969..9201fe8cd 100644
--- a/test/builtin/list/test_constructing.py
+++ b/test/builtin/list/test_constructing.py
@@ -2,6 +2,7 @@
 """
 Unit tests for mathics.builtins.list.constructing
 """
+
 from test.helper import check_evaluation
 
 import pytest
@@ -72,3 +73,59 @@ def test_range(str_expr, str_expected, failure_message):
 )
 def test_table(str_expr, str_expected, failure_message):
     check_evaluation(str_expr, str_expected, failure_message)
+
+
+@pytest.mark.parametrize(
+    ("str_expr", "str_expected", "failure_message"),
+    [
+        (None, None, None),
+        (
+            "ClearAll[l, x]; l = Table[x, {1}]; x = 1; l",
+            "{1}",
+            "A table sees a definition made after it.",
+        ),
+        (
+            "ClearAll[l, f, y]; l = Table[f[y], {1}]; f[y_] := 7; l",
+            "{7}",
+            "A table sees a rule defined after it.",
+        ),
+        (
+            "ClearAll[t, x]; t = Table[i + x, {i, 2}]; x = 1; t",
+            "{2, 3}",
+            None,
+        ),
+        ("{f /@ {}}", "{{}}", "A list of literals with pessimistic properties."),
+        ("Table[f /@ {}, {2}]", "{{}, {}}", None),
+        ("ClearAll[l, t, f, x, y]", "Null", None),
+    ],
+)
+def test_table_is_evaluated_again(str_expr, str_expected, failure_message):
+    check_evaluation(str_expr, str_expected, failure_message)
+
+
+def test_table_fully_evaluated_at_creation():
+    """A table of literal elements, like a list of numbers, is known to be
+    fully evaluated as soon as Table builds it; a table with other elements
+    is not."""
+    from mathics.builtin.list.constructing import Table
+    from mathics.core.atoms import Integer1, Integer2
+    from mathics.core.expression import Expression
+    from mathics.core.list import ListExpression
+    from mathics.core.symbols import Symbol
+    from mathics.core.systemsymbols import SymbolTimes
+
+    numbers = Table.get_result(None, [Integer1, Integer2])
+    assert numbers.elements_properties is not None
+    assert numbers.elements_properties.elements_fully_evaluated
+
+    pairs = Table.get_result(
+        None, [ListExpression(Integer1, Integer2), ListExpression(Integer2, Integer1)]
+    )
+    assert pairs.elements_properties.elements_fully_evaluated
+
+    x = Symbol("Global`x")
+    symbolic = Table.get_result(None, [x, Expression(SymbolTimes, Integer2, x)])
+    assert not (
+        symbolic.elements_properties
+        and symbolic.elements_properties.elements_fully_evaluated
+    )