diff --git a/hugr-core/src/builder/build_traits.rs b/hugr-core/src/builder/build_traits.rs
index 1cb8e242e..d04e44d79 100644
--- a/hugr-core/src/builder/build_traits.rs
+++ b/hugr-core/src/builder/build_traits.rs
@@ -777,8 +777,8 @@ fn wire_up<T: Dataflow + ?Sized>(
                 });
             };
 
-            if !OpTag::BasicBlock.is_superset(base.get_optype(src).tag())
-                && !OpTag::BasicBlock.is_superset(base.get_optype(src_sibling).tag())
+            if !OpTag::ControlFlowChild.is_superset(base.get_optype(src).tag())
+                && !OpTag::ControlFlowChild.is_superset(base.get_optype(src_sibling).tag())
             {
                 // Add a state order constraint unless one of the nodes is a CFG BasicBlock
                 base.add_other_edge(src, src_sibling);
diff --git a/hugr-core/src/hugr/views/root_checked.rs b/hugr-core/src/hugr/views/root_checked.rs
index 94ac05242..83d6aa46c 100644
--- a/hugr-core/src/hugr/views/root_checked.rs
+++ b/hugr-core/src/hugr/views/root_checked.rs
@@ -107,7 +107,7 @@ mod test {
             r,
             Err(HugrError::InvalidTag {
                 required: OpTag::Dfg,
-                actual: ops::OpTag::BasicBlock
+                actual: ops::OpTag::DataflowBlock
             })
         );
         // That didn't do anything:
diff --git a/hugr-core/src/ops/controlflow.rs b/hugr-core/src/ops/controlflow.rs
index ad60e7b86..d8f7c39bb 100644
--- a/hugr-core/src/ops/controlflow.rs
+++ b/hugr-core/src/ops/controlflow.rs
@@ -154,7 +154,7 @@ impl NamedOp for ExitBlock {
 }
 
 impl StaticTag for DataflowBlock {
-    const TAG: OpTag = OpTag::BasicBlock;
+    const TAG: OpTag = OpTag::DataflowBlock;
 }
 
 impl StaticTag for ExitBlock {
diff --git a/hugr-core/src/ops/handle.rs b/hugr-core/src/ops/handle.rs
index f7fd31ed8..d7fe16419 100644
--- a/hugr-core/src/ops/handle.rs
+++ b/hugr-core/src/ops/handle.rs
@@ -154,7 +154,7 @@ impl_nodehandle!(ModuleRootID, OpTag::ModuleRoot);
 impl_nodehandle!(ModuleID, OpTag::ModuleOp);
 impl_nodehandle!(ConstID, OpTag::Const);
 
-impl_nodehandle!(BasicBlockID, OpTag::BasicBlock);
+impl_nodehandle!(BasicBlockID, OpTag::DataflowBlock);
 
 impl<const DEF: bool> NodeHandle for FuncID<DEF> {
     const TAG: OpTag = OpTag::Function;
diff --git a/hugr-core/src/ops/tag.rs b/hugr-core/src/ops/tag.rs
index 9bc55843c..b9edcf84e 100644
--- a/hugr-core/src/ops/tag.rs
+++ b/hugr-core/src/ops/tag.rs
@@ -67,8 +67,8 @@ pub enum OpTag {
     /// A leaf operation.
     Leaf,
 
-    /// A control flow basic block.
-    BasicBlock,
+    /// A control flow basic block defining a dataflow graph.
+    DataflowBlock,
     /// A control flow exit node.
     BasicBlockExit,
 }
@@ -113,8 +113,8 @@ impl OpTag {
             OpTag::Function => &[OpTag::ModuleOp, OpTag::StaticOutput],
             OpTag::Alias => &[OpTag::ScopedDefn],
             OpTag::FuncDefn => &[OpTag::Function, OpTag::ScopedDefn, OpTag::DataflowParent],
-            OpTag::BasicBlock => &[OpTag::ControlFlowChild, OpTag::DataflowParent],
-            OpTag::BasicBlockExit => &[OpTag::BasicBlock],
+            OpTag::DataflowBlock => &[OpTag::ControlFlowChild, OpTag::DataflowParent],
+            OpTag::BasicBlockExit => &[OpTag::ControlFlowChild],
             OpTag::Case => &[OpTag::Any, OpTag::DataflowParent],
             OpTag::ModuleRoot => &[OpTag::Any],
             OpTag::Const => &[OpTag::ScopedDefn, OpTag::StaticOutput],
@@ -148,7 +148,7 @@ impl OpTag {
             OpTag::Input => "Input node",
             OpTag::Output => "Output node",
             OpTag::FuncDefn => "Function definition",
-            OpTag::BasicBlock => "Basic block",
+            OpTag::DataflowBlock => "Basic block containing a dataflow graph",
             OpTag::BasicBlockExit => "Exit basic block node",
             OpTag::Case => "Case",
             OpTag::ModuleRoot => "Module root node",
@@ -213,16 +213,20 @@ mod test {
         assert!(OpTag::None.is_superset(OpTag::None));
         assert!(OpTag::ModuleOp.is_superset(OpTag::ModuleOp));
         assert!(OpTag::DataflowChild.is_superset(OpTag::DataflowChild));
-        assert!(OpTag::BasicBlock.is_superset(OpTag::BasicBlock));
+        assert!(OpTag::ControlFlowChild.is_superset(OpTag::ControlFlowChild));
 
         assert!(OpTag::Any.is_superset(OpTag::None));
         assert!(OpTag::Any.is_superset(OpTag::ModuleOp));
         assert!(OpTag::Any.is_superset(OpTag::DataflowChild));
-        assert!(OpTag::Any.is_superset(OpTag::BasicBlock));
+        assert!(OpTag::Any.is_superset(OpTag::ControlFlowChild));
 
         assert!(!OpTag::None.is_superset(OpTag::Any));
         assert!(!OpTag::None.is_superset(OpTag::ModuleOp));
         assert!(!OpTag::None.is_superset(OpTag::DataflowChild));
-        assert!(!OpTag::None.is_superset(OpTag::BasicBlock));
+        assert!(!OpTag::None.is_superset(OpTag::ControlFlowChild));
+
+        // Other specific checks
+        assert!(!OpTag::DataflowParent.is_superset(OpTag::BasicBlockExit));
+        assert!(!OpTag::DataflowParent.is_superset(OpTag::Cfg));
     }
 }
diff --git a/hugr-core/src/ops/validate.rs b/hugr-core/src/ops/validate.rs
index 8f2e077fb..d56818b55 100644
--- a/hugr-core/src/ops/validate.rs
+++ b/hugr-core/src/ops/validate.rs
@@ -110,7 +110,7 @@ impl ValidateOp for super::CFG {
     fn validity_flags(&self) -> OpValidityFlags {
         OpValidityFlags {
             allowed_children: OpTag::ControlFlowChild,
-            allowed_first_child: OpTag::BasicBlock,
+            allowed_first_child: OpTag::DataflowBlock,
             allowed_second_child: OpTag::BasicBlockExit,
             requires_children: true,
             requires_dag: false,