diff --git a/mypy/semanal.py b/mypy/semanal.py
index 8771fb768d80..675ea9681c19 100644
--- a/mypy/semanal.py
+++ b/mypy/semanal.py
@@ -1544,7 +1544,7 @@ def process_typevar_declaration(self, s: AssignmentStmt) -> None:
         res = self.process_typevar_parameters(call.args[1 + n_values:],
                                               call.arg_names[1 + n_values:],
                                               call.arg_kinds[1 + n_values:],
-                                              bool(values),
+                                              n_values,
                                               s)
         if res is None:
             return
@@ -1591,8 +1591,9 @@ def get_typevar_declaration(self, s: AssignmentStmt) -> Optional[CallExpr]:
     def process_typevar_parameters(self, args: List[Expression],
                                    names: List[Optional[str]],
                                    kinds: List[int],
-                                   has_values: bool,
+                                   num_values: int,
                                    context: Context) -> Optional[Tuple[int, Type]]:
+        has_values = (num_values > 0)
         covariant = False
         contravariant = False
         upper_bound = self.object_type()   # type: Type
@@ -1642,6 +1643,9 @@ def process_typevar_parameters(self, args: List[Expression],
         if covariant and contravariant:
             self.fail("TypeVar cannot be both covariant and contravariant", context)
             return None
+        elif num_values == 1:
+            self.fail("TypeVar cannot have only a single constraint", context)
+            return None
         elif covariant:
             variance = COVARIANT
         elif contravariant:
diff --git a/test-data/unit/check-bound.test b/test-data/unit/check-bound.test
index ee935aed8bdd..bfe04e0cfb67 100644
--- a/test-data/unit/check-bound.test
+++ b/test-data/unit/check-bound.test
@@ -142,12 +142,12 @@ class A(A0):
 class B(A):
     def baz(self) -> None: pass
 
-T = TypeVar('T', A)
+T = TypeVar('T', bound=A)
 
 def f(x: T) -> T:
     x.foo()
     x.bar()
-    x.baz()  # E: "A" has no attribute "baz"
+    x.baz()  # E: "T" has no attribute "baz"
     x.a
     x.b
     return x
diff --git a/test-data/unit/check-classes.test b/test-data/unit/check-classes.test
index bdfa2de9b340..7db2c2b88d66 100644
--- a/test-data/unit/check-classes.test
+++ b/test-data/unit/check-classes.test
@@ -1458,13 +1458,12 @@ main:6: error: Signatures of "__radd__" of "B" and "__add__" of "X" are unsafely
 
 [case testUnsafeOverlappingWithLineNo]
 from typing import TypeVar
-T = TypeVar('T', Real)
 class Real:
     def __add__(self, other): ...
 class Fraction(Real):
-    def __radd__(self, other: T) -> T: ...
+    def __radd__(self, other: Real) -> Real: ...
 [out]
-main:6: error: Signatures of "__radd__" of "Fraction" and "__add__" of "Real" are unsafely overlapping
+main:5: error: Signatures of "__radd__" of "Fraction" and "__add__" of "Real" are unsafely overlapping
 
 [case testOverlappingNormalAndInplaceOperatorMethod]
 import typing
diff --git a/test-data/unit/check-typevar-values.test b/test-data/unit/check-typevar-values.test
index 69feab2059e4..34f5501f0a23 100644
--- a/test-data/unit/check-typevar-values.test
+++ b/test-data/unit/check-typevar-values.test
@@ -493,7 +493,7 @@ def outer(x: T) -> T:
 [case testClassMemberTypeVarInFunctionBody]
 from typing import TypeVar
 class C:
-    T = TypeVar('T', int)
+    T = TypeVar('T', bound=int)
     def f(self, x: T) -> T:
         A = C.T
         return x
diff --git a/test-data/unit/semanal-errors.test b/test-data/unit/semanal-errors.test
index 06fd3d0dd226..f7de00d1a40b 100644
--- a/test-data/unit/semanal-errors.test
+++ b/test-data/unit/semanal-errors.test
@@ -968,10 +968,11 @@ a = TypeVar()       # E: Too few arguments for TypeVar()
 b = TypeVar(x='b')  # E: TypeVar() expects a string literal as first argument
 c = TypeVar(1)      # E: TypeVar() expects a string literal as first argument
 d = TypeVar('D')    # E: String argument 1 'D' to TypeVar(...) does not match variable name 'd'
-e = TypeVar('e', int, str, x=1) # E: Unexpected argument to TypeVar(): x
-f = TypeVar('f', (int, str)) # E: Type expected
-g = TypeVar('g', x=(int, str)) # E: Unexpected argument to TypeVar(): x
-h = TypeVar('h', bound=1) # E: TypeVar 'bound' must be a type
+e = TypeVar('e', int, str, x=1)   # E: Unexpected argument to TypeVar(): x
+f = TypeVar('f', (int, str), int) # E: Type expected
+g = TypeVar('g', int)             # E: TypeVar cannot have only a single constraint
+h = TypeVar('h', x=(int, str))    # E: Unexpected argument to TypeVar(): x
+i = TypeVar('i', bound=1)         # E: TypeVar 'bound' must be a type
 [out]
 
 [case testMoreInvalidTypevarArguments]