diff --git a/docs/qapi-code-gen.txt b/docs/qapi-code-gen.txt
index 128f074a2de49e7cf200a2ff85487d20822ded05..999f3b98f021d2af25c2d7fd47873f49b42a39ff 100644
--- a/docs/qapi-code-gen.txt
+++ b/docs/qapi-code-gen.txt
@@ -187,11 +187,11 @@ prevent incomplete include files.
 
 Usage: { 'struct': STRING, 'data': DICT, '*base': STRUCT-NAME }
 
-A struct is a dictionary containing a single 'data' key whose
-value is a dictionary.  This corresponds to a struct in C or an Object
-in JSON. Each value of the 'data' dictionary must be the name of a
-type, or a one-element array containing a type name.  An example of a
-struct is:
+A struct is a dictionary containing a single 'data' key whose value is
+a dictionary; the dictionary may be empty.  This corresponds to a
+struct in C or an Object in JSON. Each value of the 'data' dictionary
+must be the name of a type, or a one-element array containing a type
+name.  An example of a struct is:
 
  { 'struct': 'MyType',
    'data': { 'member1': 'str', 'member2': 'int', '*member3': 'str' } }
@@ -288,9 +288,10 @@ or:    { 'union': STRING, 'data': DICT, 'base': STRUCT-NAME,
 
 Union types are used to let the user choose between several different
 variants for an object.  There are two flavors: simple (no
-discriminator or base), flat (both discriminator and base).  A union
+discriminator or base), and flat (both discriminator and base).  A union
 type is defined using a data dictionary as explained in the following
-paragraphs.
+paragraphs.  The data dictionary for either type of union must not
+be empty.
 
 A simple union type defines a mapping from automatic discriminator
 values to data types like in this example:
diff --git a/scripts/qapi.py b/scripts/qapi.py
index f40dc9e777d809b387a833dd492e2d839459d94b..f97236f5098aea44f316090ae176fe153c39aa38 100644
--- a/scripts/qapi.py
+++ b/scripts/qapi.py
@@ -590,7 +590,10 @@ def check_union(expr, expr_info):
                                 "Discriminator '%s' must be of enumeration "
                                 "type" % discriminator)
 
-    # Check every branch
+    # Check every branch; don't allow an empty union
+    if len(members) == 0:
+        raise QAPIExprError(expr_info,
+                            "Union '%s' cannot have empty 'data'" % name)
     for (key, value) in members.items():
         check_name(expr_info, "Member of union '%s'" % name, key)
 
@@ -613,7 +616,11 @@ def check_alternate(expr, expr_info):
     members = expr['data']
     types_seen = {}
 
-    # Check every branch
+    # Check every branch; require at least two branches
+    if len(members) < 2:
+        raise QAPIExprError(expr_info,
+                            "Alternate '%s' should have at least two branches "
+                            "in 'data'" % name)
     for (key, value) in members.items():
         check_name(expr_info, "Member of alternate '%s'" % name, key)
 
@@ -1059,6 +1066,7 @@ class QAPISchemaObjectTypeVariants(object):
         assert bool(tag_member) != bool(tag_name)
         assert (isinstance(tag_name, str) or
                 isinstance(tag_member, QAPISchemaObjectTypeMember))
+        assert len(variants) > 0
         for v in variants:
             assert isinstance(v, QAPISchemaObjectTypeVariant)
         self.tag_name = tag_name
diff --git a/tests/qapi-schema/alternate-empty.err b/tests/qapi-schema/alternate-empty.err
index e69de29bb2d1d6434b8b29ae775ad8c2e48c5391..bb06c5bfec08a9b31324102c75790f2f05574319 100644
--- a/tests/qapi-schema/alternate-empty.err
+++ b/tests/qapi-schema/alternate-empty.err
@@ -0,0 +1 @@
+tests/qapi-schema/alternate-empty.json:2: Alternate 'Alt' should have at least two branches in 'data'
diff --git a/tests/qapi-schema/alternate-empty.exit b/tests/qapi-schema/alternate-empty.exit
index 573541ac9702dd3969c9bc859d2b91ec1f7e6e56..d00491fd7e5bb6fa28c517a0bb32b8b506539d4d 100644
--- a/tests/qapi-schema/alternate-empty.exit
+++ b/tests/qapi-schema/alternate-empty.exit
@@ -1 +1 @@
-0
+1
diff --git a/tests/qapi-schema/alternate-empty.json b/tests/qapi-schema/alternate-empty.json
index db3820f841a5ebb8600acb5aaee7055b697f589f..fff15baf16c2ef48efc4619d21d4a3ded29e2325 100644
--- a/tests/qapi-schema/alternate-empty.json
+++ b/tests/qapi-schema/alternate-empty.json
@@ -1,2 +1,2 @@
-# FIXME - alternates should list at least two types to be useful
+# alternates must list at least two types to be useful
 { 'alternate': 'Alt', 'data': { 'i': 'int' } }
diff --git a/tests/qapi-schema/alternate-empty.out b/tests/qapi-schema/alternate-empty.out
index f78f174111c18255a158ac2c58f9d495516b6b1c..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 100644
--- a/tests/qapi-schema/alternate-empty.out
+++ b/tests/qapi-schema/alternate-empty.out
@@ -1,5 +0,0 @@
-object :empty
-alternate Alt
-    case i: int
-enum QType ['none', 'qnull', 'qint', 'qstring', 'qdict', 'qlist', 'qfloat', 'qbool']
-    prefix QTYPE
diff --git a/tests/qapi-schema/flat-union-empty.err b/tests/qapi-schema/flat-union-empty.err
index e69de29bb2d1d6434b8b29ae775ad8c2e48c5391..15754f54eb9251724eaddb1dc98085fc941b781c 100644
--- a/tests/qapi-schema/flat-union-empty.err
+++ b/tests/qapi-schema/flat-union-empty.err
@@ -0,0 +1 @@
+tests/qapi-schema/flat-union-empty.json:4: Union 'Union' cannot have empty 'data'
diff --git a/tests/qapi-schema/flat-union-empty.exit b/tests/qapi-schema/flat-union-empty.exit
index 573541ac9702dd3969c9bc859d2b91ec1f7e6e56..d00491fd7e5bb6fa28c517a0bb32b8b506539d4d 100644
--- a/tests/qapi-schema/flat-union-empty.exit
+++ b/tests/qapi-schema/flat-union-empty.exit
@@ -1 +1 @@
-0
+1
diff --git a/tests/qapi-schema/flat-union-empty.json b/tests/qapi-schema/flat-union-empty.json
index 67dd2978eb173ac639abb7c95306ebb1282a203d..77f1d9abfb8f9b39a0a9dd9a03be3cb4e4343c15 100644
--- a/tests/qapi-schema/flat-union-empty.json
+++ b/tests/qapi-schema/flat-union-empty.json
@@ -1,4 +1,4 @@
-# FIXME - flat unions should not be empty
+# flat unions cannot be empty
 { 'enum': 'Empty', 'data': [ ] }
 { 'struct': 'Base', 'data': { 'type': 'Empty' } }
 { 'union': 'Union', 'base': 'Base', 'discriminator': 'type', 'data': { } }
diff --git a/tests/qapi-schema/flat-union-empty.out b/tests/qapi-schema/flat-union-empty.out
index eade2d5ac6ec8e1c74d20d0ce58be97b65a3402f..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 100644
--- a/tests/qapi-schema/flat-union-empty.out
+++ b/tests/qapi-schema/flat-union-empty.out
@@ -1,9 +0,0 @@
-object :empty
-object Base
-    member type: Empty optional=False
-enum Empty []
-enum QType ['none', 'qnull', 'qint', 'qstring', 'qdict', 'qlist', 'qfloat', 'qbool']
-    prefix QTYPE
-object Union
-    base Base
-    tag type
diff --git a/tests/qapi-schema/union-empty.err b/tests/qapi-schema/union-empty.err
index e69de29bb2d1d6434b8b29ae775ad8c2e48c5391..12c20221bdfb6f7b046a7deaaf1074aa6126b651 100644
--- a/tests/qapi-schema/union-empty.err
+++ b/tests/qapi-schema/union-empty.err
@@ -0,0 +1 @@
+tests/qapi-schema/union-empty.json:2: Union 'Union' cannot have empty 'data'
diff --git a/tests/qapi-schema/union-empty.exit b/tests/qapi-schema/union-empty.exit
index 573541ac9702dd3969c9bc859d2b91ec1f7e6e56..d00491fd7e5bb6fa28c517a0bb32b8b506539d4d 100644
--- a/tests/qapi-schema/union-empty.exit
+++ b/tests/qapi-schema/union-empty.exit
@@ -1 +1 @@
-0
+1
diff --git a/tests/qapi-schema/union-empty.json b/tests/qapi-schema/union-empty.json
index 1785007113360147aa09969fce5351ecdfd4c7ac..1f0b13ca21ae25d34b9d67da84df14b88f35e959 100644
--- a/tests/qapi-schema/union-empty.json
+++ b/tests/qapi-schema/union-empty.json
@@ -1,2 +1,2 @@
-# FIXME - unions should not be empty
+# unions cannot be empty
 { 'union': 'Union', 'data': { } }
diff --git a/tests/qapi-schema/union-empty.out b/tests/qapi-schema/union-empty.out
index bdf17e5b29500650723dc8c06f5341ad03640d28..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 100644
--- a/tests/qapi-schema/union-empty.out
+++ b/tests/qapi-schema/union-empty.out
@@ -1,6 +0,0 @@
-object :empty
-enum QType ['none', 'qnull', 'qint', 'qstring', 'qdict', 'qlist', 'qfloat', 'qbool']
-    prefix QTYPE
-object Union
-    member type: UnionKind optional=False
-enum UnionKind []