diff --git a/hugr-py/src/hugr/serialization/ops.py b/hugr-py/src/hugr/serialization/ops.py
index 9490a5c57..8743086fd 100644
--- a/hugr-py/src/hugr/serialization/ops.py
+++ b/hugr-py/src/hugr/serialization/ops.py
@@ -300,13 +300,6 @@ class LoadConstant(DataflowOp):
     datatype: Type
 
 
-class LeafOpBase(DataflowOp):
-    """Simple operation that has only value inputs+outputs and (potentially) StateOrder
-    edges."""
-
-    op: Literal["LeafOp"] = "LeafOp"
-
-
 class DFG(DataflowOp):
     """A simply nested dataflow graph."""
 
@@ -398,11 +391,11 @@ def insert_port_types(self, inputs: TypeRow, outputs: TypeRow) -> None:
 # -----------------------------------------
 
 
-class CustomOp(LeafOpBase):
+class CustomOp(DataflowOp):
     """A user-defined operation that can be downcasted by the extensions that define
     it."""
 
-    lop: Literal["CustomOp"] = "CustomOp"
+    op: Literal["CustomOp"] = "CustomOp"
     extension: ExtensionId
     op_name: str
     signature: tys.FunctionType = Field(default_factory=tys.FunctionType.empty)
@@ -425,10 +418,10 @@ class Config:
         }
 
 
-class Noop(LeafOpBase):
+class Noop(DataflowOp):
     """A no-op operation."""
 
-    lop: Literal["Noop"] = "Noop"
+    op: Literal["Noop"] = "Noop"
     ty: Type
 
     def insert_port_types(self, in_types: TypeRow, out_types: TypeRow) -> None:
@@ -438,10 +431,10 @@ def insert_port_types(self, in_types: TypeRow, out_types: TypeRow) -> None:
         self.ty = in_types[0]
 
 
-class MakeTuple(LeafOpBase):
+class MakeTuple(DataflowOp):
     """An operation that packs all its inputs into a tuple."""
 
-    lop: Literal["MakeTuple"] = "MakeTuple"
+    op: Literal["MakeTuple"] = "MakeTuple"
     tys: TypeRow = Field(default_factory=list)
 
     def insert_port_types(self, in_types: TypeRow, out_types: TypeRow) -> None:
@@ -451,56 +444,30 @@ def insert_port_types(self, in_types: TypeRow, out_types: TypeRow) -> None:
         self.tys = list(in_types)
 
 
-class UnpackTuple(LeafOpBase):
+class UnpackTuple(DataflowOp):
     """An operation that packs all its inputs into a tuple."""
 
-    lop: Literal["UnpackTuple"] = "UnpackTuple"
+    op: Literal["UnpackTuple"] = "UnpackTuple"
     tys: TypeRow = Field(default_factory=list)
 
     def insert_port_types(self, in_types: TypeRow, out_types: TypeRow) -> None:
         self.tys = list(out_types)
 
 
-class Tag(LeafOpBase):
+class Tag(DataflowOp):
     """An operation that creates a tagged sum value from one of its variants."""
 
-    lop: Literal["Tag"] = "Tag"
+    op: Literal["Tag"] = "Tag"
     tag: int  # The variant to create.
     variants: TypeRow  # The variants of the sum type.
 
 
-class TypeApply(LeafOpBase):
+class Lift(DataflowOp):
     """Fixes some TypeParams of a polymorphic type by providing TypeArgs."""
 
-    lop: Literal["TypeApply"] = "TypeApply"
-    ta: "TypeApplication"
-
-
-class TypeApplication(BaseModel):
-    """Records details of an application of a PolyFuncType to some TypeArgs and the
-    result (a less-, but still potentially-, polymorphic type).
-    """
-
-    input: PolyFuncType
-    args: list[tys.TypeTypeArg]
-    output: PolyFuncType
-
-    class Config:
-        # Needed to avoid random '\n's in the pydantic description
-        json_schema_extra = {
-            "description": (
-                "Records details of an application of a PolyFuncType to some TypeArgs "
-                "and the result (a less-, but still potentially-, polymorphic type)."
-            )
-        }
-
-
-class LeafOp(RootModel):
-    """A constant operation."""
-
-    root: CustomOp | Noop | MakeTuple | UnpackTuple | Tag | TypeApply = Field(
-        discriminator="lop"
-    )
+    op: Literal["Lift"] = "Lift"
+    type_row: TypeRow
+    new_extension: ExtensionId
 
 
 class OpType(RootModel):
@@ -522,7 +489,12 @@ class OpType(RootModel):
         | Call
         | CallIndirect
         | LoadConstant
-        | LeafOp
+        | CustomOp
+        | Noop
+        | MakeTuple
+        | UnpackTuple
+        | Tag
+        | Lift
         | DFG
     ) = Field(discriminator="op")
 
diff --git a/specification/schema/hugr_schema_v1.json b/specification/schema/hugr_schema_v1.json
index 6b6731be5..e634d4076 100644
--- a/specification/schema/hugr_schema_v1.json
+++ b/specification/schema/hugr_schema_v1.json
@@ -255,14 +255,9 @@
                     "$ref": "#/$defs/ExtensionSet"
                 },
                 "op": {
-                    "const": "LeafOp",
-                    "default": "LeafOp",
-                    "title": "Op"
-                },
-                "lop": {
                     "const": "CustomOp",
                     "default": "CustomOp",
-                    "title": "Lop"
+                    "title": "Op"
                 },
                 "extension": {
                     "title": "Extension",
@@ -674,40 +669,40 @@
             "title": "Input",
             "type": "object"
         },
-        "LeafOp": {
-            "description": "A constant operation.",
-            "discriminator": {
-                "mapping": {
-                    "CustomOp": "#/$defs/CustomOp",
-                    "MakeTuple": "#/$defs/MakeTuple",
-                    "Noop": "#/$defs/Noop",
-                    "Tag": "#/$defs/Tag",
-                    "TypeApply": "#/$defs/TypeApply",
-                    "UnpackTuple": "#/$defs/UnpackTuple"
-                },
-                "propertyName": "lop"
-            },
-            "oneOf": [
-                {
-                    "$ref": "#/$defs/CustomOp"
-                },
-                {
-                    "$ref": "#/$defs/Noop"
+        "Lift": {
+            "description": "Fixes some TypeParams of a polymorphic type by providing TypeArgs.",
+            "properties": {
+                "parent": {
+                    "title": "Parent",
+                    "type": "integer"
                 },
-                {
-                    "$ref": "#/$defs/MakeTuple"
+                "input_extensions": {
+                    "$ref": "#/$defs/ExtensionSet"
                 },
-                {
-                    "$ref": "#/$defs/UnpackTuple"
+                "op": {
+                    "const": "Lift",
+                    "default": "Lift",
+                    "title": "Op"
                 },
-                {
-                    "$ref": "#/$defs/Tag"
+                "type_row": {
+                    "items": {
+                        "$ref": "#/$defs/Type"
+                    },
+                    "title": "Type Row",
+                    "type": "array"
                 },
-                {
-                    "$ref": "#/$defs/TypeApply"
+                "new_extension": {
+                    "title": "New Extension",
+                    "type": "string"
                 }
+            },
+            "required": [
+                "parent",
+                "type_row",
+                "new_extension"
             ],
-            "title": "LeafOp"
+            "title": "Lift",
+            "type": "object"
         },
         "ListParam": {
             "properties": {
@@ -763,14 +758,9 @@
                     "$ref": "#/$defs/ExtensionSet"
                 },
                 "op": {
-                    "const": "LeafOp",
-                    "default": "LeafOp",
-                    "title": "Op"
-                },
-                "lop": {
                     "const": "MakeTuple",
                     "default": "MakeTuple",
-                    "title": "Lop"
+                    "title": "Op"
                 },
                 "tys": {
                     "items": {
@@ -819,14 +809,9 @@
                     "$ref": "#/$defs/ExtensionSet"
                 },
                 "op": {
-                    "const": "LeafOp",
-                    "default": "LeafOp",
-                    "title": "Op"
-                },
-                "lop": {
                     "const": "Noop",
                     "default": "Noop",
-                    "title": "Lop"
+                    "title": "Op"
                 },
                 "ty": {
                     "$ref": "#/$defs/Type"
@@ -849,17 +834,22 @@
                     "Case": "#/$defs/Case",
                     "Conditional": "#/$defs/Conditional",
                     "Const": "#/$defs/Const",
+                    "CustomOp": "#/$defs/CustomOp",
                     "DFG": "#/$defs/DFG",
                     "DataflowBlock": "#/$defs/DataflowBlock",
                     "ExitBlock": "#/$defs/ExitBlock",
                     "FuncDecl": "#/$defs/FuncDecl",
                     "FuncDefn": "#/$defs/FuncDefn",
                     "Input": "#/$defs/Input",
-                    "LeafOp": "#/$defs/LeafOp",
+                    "Lift": "#/$defs/Lift",
                     "LoadConstant": "#/$defs/LoadConstant",
+                    "MakeTuple": "#/$defs/MakeTuple",
                     "Module": "#/$defs/Module",
+                    "Noop": "#/$defs/Noop",
                     "Output": "#/$defs/Output",
-                    "TailLoop": "#/$defs/TailLoop"
+                    "Tag": "#/$defs/Tag",
+                    "TailLoop": "#/$defs/TailLoop",
+                    "UnpackTuple": "#/$defs/UnpackTuple"
                 },
                 "propertyName": "op"
             },
@@ -910,7 +900,22 @@
                     "$ref": "#/$defs/LoadConstant"
                 },
                 {
-                    "$ref": "#/$defs/LeafOp"
+                    "$ref": "#/$defs/CustomOp"
+                },
+                {
+                    "$ref": "#/$defs/Noop"
+                },
+                {
+                    "$ref": "#/$defs/MakeTuple"
+                },
+                {
+                    "$ref": "#/$defs/UnpackTuple"
+                },
+                {
+                    "$ref": "#/$defs/Tag"
+                },
+                {
+                    "$ref": "#/$defs/Lift"
                 },
                 {
                     "$ref": "#/$defs/DFG"
@@ -1146,14 +1151,9 @@
                     "$ref": "#/$defs/ExtensionSet"
                 },
                 "op": {
-                    "const": "LeafOp",
-                    "default": "LeafOp",
-                    "title": "Op"
-                },
-                "lop": {
                     "const": "Tag",
                     "default": "Tag",
-                    "title": "Lop"
+                    "title": "Op"
                 },
                 "tag": {
                     "title": "Tag",
@@ -1315,62 +1315,6 @@
             ],
             "title": "Type"
         },
-        "TypeApplication": {
-            "description": "Records details of an application of a PolyFuncType to some TypeArgs and the result (a less-, but still potentially-, polymorphic type).",
-            "properties": {
-                "input": {
-                    "$ref": "#/$defs/PolyFuncType"
-                },
-                "args": {
-                    "items": {
-                        "$ref": "#/$defs/TypeTypeArg"
-                    },
-                    "title": "Args",
-                    "type": "array"
-                },
-                "output": {
-                    "$ref": "#/$defs/PolyFuncType"
-                }
-            },
-            "required": [
-                "input",
-                "args",
-                "output"
-            ],
-            "title": "TypeApplication",
-            "type": "object"
-        },
-        "TypeApply": {
-            "description": "Fixes some TypeParams of a polymorphic type by providing TypeArgs.",
-            "properties": {
-                "parent": {
-                    "title": "Parent",
-                    "type": "integer"
-                },
-                "input_extensions": {
-                    "$ref": "#/$defs/ExtensionSet"
-                },
-                "op": {
-                    "const": "LeafOp",
-                    "default": "LeafOp",
-                    "title": "Op"
-                },
-                "lop": {
-                    "const": "TypeApply",
-                    "default": "TypeApply",
-                    "title": "Lop"
-                },
-                "ta": {
-                    "$ref": "#/$defs/TypeApplication"
-                }
-            },
-            "required": [
-                "parent",
-                "ta"
-            ],
-            "title": "TypeApply",
-            "type": "object"
-        },
         "TypeArg": {
             "description": "A type argument.",
             "discriminator": {
@@ -1523,14 +1467,9 @@
                     "$ref": "#/$defs/ExtensionSet"
                 },
                 "op": {
-                    "const": "LeafOp",
-                    "default": "LeafOp",
-                    "title": "Op"
-                },
-                "lop": {
                     "const": "UnpackTuple",
                     "default": "UnpackTuple",
-                    "title": "Lop"
+                    "title": "Op"
                 },
                 "tys": {
                     "items": {