diff --git a/astroid/brain/brain_builtin_inference.py b/astroid/brain/brain_builtin_inference.py
index a2ca95514..9eec700da 100644
--- a/astroid/brain/brain_builtin_inference.py
+++ b/astroid/brain/brain_builtin_inference.py
@@ -842,15 +842,35 @@ def infer_str(node, context: InferenceContext | None = None) -> nodes.Const:
 
     :param nodes.Call node: str() call to infer
     :param context.InferenceContext: node context
-    :rtype nodes.Const: a Const containing an empty string
+    :rtype nodes.Const:
+        a Const containing a stringified value of str() call if possible, else an empty string
     """
     call = arguments.CallSite.from_call(node, context=context)
     if call.keyword_arguments:
         raise UseInferenceDefault("TypeError: str() must take no keyword arguments")
+
+    fallback = nodes.Const("")
+
+    if not call.positional_arguments:
+        return fallback
+
+    # Accept only if all inferred values resolve to the same string
+    candidates: set[str] = set()
     try:
-        return nodes.Const("")
-    except (AstroidTypeError, InferenceError) as exc:
-        raise UseInferenceDefault(str(exc)) from exc
+        for inferred in call.positional_arguments[0].infer(context=context):
+            if not isinstance(inferred, nodes.Const):
+                return fallback
+
+            try:
+                candidates.add(str(inferred.value))
+            except ValueError:
+                return fallback
+    except InferenceError:
+        return fallback
+
+    if len(candidates) == 1:
+        return nodes.Const(candidates.pop())
+    return fallback
 
 
 def infer_int(node, context: InferenceContext | None = None):
diff --git a/tests/brain/test_brain.py b/tests/brain/test_brain.py
index 0b60ac264..b661f4495 100644
--- a/tests/brain/test_brain.py
+++ b/tests/brain/test_brain.py
@@ -1407,6 +1407,7 @@ def test_infer_str() -> None:
     str(s) #@
     str('a') #@
     str(some_object()) #@
+    str(7**10000) #@
     """)
     for node in ast_nodes:
         inferred = next(node.infer())
@@ -1420,6 +1421,37 @@ def test_infer_str() -> None:
     assert inferred.qname() == "builtins.str"
 
 
+def test_infer_str_const() -> None:
+    ast_nodes = astroid.extract_node("""
+    str('') #@
+    str('a') #@
+    str(1) #@
+    str(True) #@
+    str(False) #@
+    str(None) #@
+    str(4.33) #@
+    str(...) #@
+    str(2 + 2) #@
+    str() #@
+    str(int) #@
+    str(2 if unknown() else 3) #@
+    """)
+
+    inferred = list(node.inferred()[0].value for node in ast_nodes)
+    assert inferred[0] == ""
+    assert inferred[1] == "a"
+    assert inferred[2] == "1"
+    assert inferred[3] == "True"
+    assert inferred[4] == "False"
+    assert inferred[5] == "None"
+    assert inferred[6] == "4.33"
+    assert inferred[7] == "Ellipsis"
+    assert inferred[8] == "4"
+    assert inferred[9] == ""
+    assert inferred[10] == ""
+    assert inferred[11] == ""
+
+
 def test_infer_int() -> None:
     ast_nodes = astroid.extract_node("""
     int(0) #@