diff --git a/tests/functional/syntax/test_as_wei_value.py b/tests/functional/syntax/test_as_wei_value.py
index fd5f9e20ba..4ed3f0a224 100644
--- a/tests/functional/syntax/test_as_wei_value.py
+++ b/tests/functional/syntax/test_as_wei_value.py
@@ -61,6 +61,24 @@ def foo():
     """,
         InvalidLiteral,
     ),
+    (
+        """
+FOO: constant(uint256) = as_wei_value(5, szabo)
+    """,
+        ArgumentException,
+    ),
+    (
+        """
+FOO: constant(uint256) = as_wei_value(5, "szaboo")
+    """,
+        ArgumentException,
+    ),
+    (
+        """
+FOO: constant(uint256) = as_wei_value(-1, "szabo")
+    """,
+        InvalidLiteral,
+    ),
 ]
 
 
diff --git a/tests/functional/syntax/test_epsilon.py b/tests/functional/syntax/test_epsilon.py
new file mode 100644
index 0000000000..73369d4b8a
--- /dev/null
+++ b/tests/functional/syntax/test_epsilon.py
@@ -0,0 +1,14 @@
+import pytest
+
+from vyper.exceptions import InvalidType
+
+fail_list = [
+    """
+FOO: constant(address) = epsilon(address)
+    """
+]
+
+
+@pytest.mark.parametrize("bad_code", fail_list)
+def test_block_fail(assert_compile_failed, get_contract_with_gas_estimation, bad_code):
+    assert_compile_failed(lambda: get_contract_with_gas_estimation(bad_code), InvalidType)
diff --git a/tests/functional/syntax/test_method_id.py b/tests/functional/syntax/test_method_id.py
index 1a59f6bd6e..da67e67fe3 100644
--- a/tests/functional/syntax/test_method_id.py
+++ b/tests/functional/syntax/test_method_id.py
@@ -1,7 +1,7 @@
 import pytest
 
 from vyper import compiler
-from vyper.exceptions import InvalidLiteral
+from vyper.exceptions import InvalidLiteral, InvalidType
 
 fail_list = [
     (
@@ -11,7 +11,19 @@ def foo():
     a: Bytes[4] = method_id("bar ()")
     """,
         InvalidLiteral,
-    )
+    ),
+    (
+        """
+FOO: constant(Bytes[4]) = method_id(1)
+    """,
+        InvalidType,
+    ),
+    (
+        """
+FOO: constant(Bytes[4]) = method_id("bar ()")
+    """,
+        InvalidLiteral,
+    ),
 ]
 
 
diff --git a/tests/functional/syntax/test_minmax_value.py b/tests/functional/syntax/test_minmax_value.py
index e154cad23f..14b61e2f0a 100644
--- a/tests/functional/syntax/test_minmax_value.py
+++ b/tests/functional/syntax/test_minmax_value.py
@@ -13,6 +13,9 @@ def foo():
 def foo():
     a: address = max_value(address)
     """,
+    """
+FOO: constant(address) = min_value(address)
+    """,
 ]
 
 
diff --git a/vyper/builtins/functions.py b/vyper/builtins/functions.py
index 2aea650ea0..9106c0def1 100644
--- a/vyper/builtins/functions.py
+++ b/vyper/builtins/functions.py
@@ -742,6 +742,11 @@ def fetch_call_return(self, node):
         type_ = self.infer_kwarg_types(node)["output_type"].typedef
         return type_
 
+    def infer_arg_types(self, node, expected_return_typ=None):
+        # call `evaluate` for its typechecking side effects
+        self.evaluate(node)
+        return [self._inputs[0][1]]
+
     def infer_kwarg_types(self, node):
         # If `output_type` is not given, default to `Bytes[4]`
         output_typedef = TYPE_T(BytesT(4))
@@ -977,16 +982,12 @@ class AsWeiValue(BuiltinFunction):
         ("kether", "grand"): 10**21,
     }
 
-    def _get_denomination_node(self, node):
+    def get_denomination(self, node):
         value = node.args[1]._metadata.get("folded_value")
         if not isinstance(value, vy_ast.Str):
             raise ArgumentException(
                 "Wei denomination must be given as a literal string", node.args[1]
             )
-        return value
-
-    def get_denomination(self, node):
-        value = self._get_denomination_node(node)
         try:
             denom = next(v for k, v in self.wei_denoms.items() if value.value in k)
         except StopIteration:
@@ -1013,9 +1014,12 @@ def fetch_call_return(self, node):
         return self._return_type
 
     def infer_arg_types(self, node, expected_return_typ=None):
-        # raise a better error message by first calling this function
-        # for its side effects of checking the denom
-        self._get_denomination_node(node)
+        # call `evaluate` for its typechecking side effects`
+        try:
+            self.evaluate(node)
+        except UnfoldableNode:
+            pass
+
         self._validate_arg_types(node)
         # return a concrete type instead of abstract type
         value_type = get_possible_types_from_node(node.args[0]).pop()
@@ -2585,6 +2589,12 @@ def evaluate(self, node):
         ret._metadata["type"] = input_type
         return ret
 
+    def infer_arg_types(self, node, expected_return_typ=None):
+        # call `evaluate` for its typechecking side effects
+        self.evaluate(node)
+        input_typedef = TYPE_T(type_from_annotation(node.args[0]))
+        return [input_typedef]
+
 
 class MinValue(_MinMaxValue):
     _id = "min_value"
diff --git a/vyper/semantics/analysis/module.py b/vyper/semantics/analysis/module.py
index 6952bb1ee4..651c92c4aa 100644
--- a/vyper/semantics/analysis/module.py
+++ b/vyper/semantics/analysis/module.py
@@ -240,13 +240,13 @@ def _validate_self_namespace():
                 raise exc.with_annotation(node) from None
 
         if node.is_constant:
+            ExprVisitor().visit(node.value, type_)
             if not node.value:
                 raise VariableDeclarationException("Constant must be declared with a value", node)
             if not check_variable_constancy(node.value, VariableConstancy.COMPILE_TIME_CONSTANT):
                 raise StateAccessViolation("Value must be a literal", node.value)
 
             validate_expected_type(node.value, type_)
-            ExprVisitor().visit(node.value, type_)
             _validate_self_namespace()
 
             return _finalize()