diff --git a/hugr-passes/src/const_fold.rs b/hugr-passes/src/const_fold.rs
index 7552ed36f..37f3eb6e0 100644
--- a/hugr-passes/src/const_fold.rs
+++ b/hugr-passes/src/const_fold.rs
@@ -3,17 +3,14 @@
 //! An (example) use of the [dataflow analysis framework](super::dataflow).
 
 pub mod value_handle;
+use itertools::{Either, Itertools};
 use std::{collections::HashMap, sync::Arc};
 use thiserror::Error;
 
 use hugr_core::{
-    hugr::{
-        hugrmut::HugrMut,
-        views::{DescendantsGraph, ExtractHugr, HierarchyView},
-    },
+    hugr::hugrmut::HugrMut,
     ops::{
-        constant::OpaqueValue, handle::FuncID, Const, DataflowOpTrait, ExtensionOp, LoadConstant,
-        OpType, Value,
+        constant::OpaqueValue, Const, DataflowOpTrait, ExtensionOp, LoadConstant, OpType, Value,
     },
     types::{EdgeKind, TypeArg},
     HugrView, IncomingPort, Node, NodeIndex, OutgoingPort, PortIndex, Wire,
@@ -207,14 +204,7 @@ pub fn constant_fold_pass<H: HugrMut>(h: &mut H) {
 
 struct ConstFoldContext<'a, H>(&'a H);
 
-impl<H: HugrView> std::ops::Deref for ConstFoldContext<'_, H> {
-    type Target = H;
-    fn deref(&self) -> &H {
-        self.0
-    }
-}
-
-impl<H: HugrView<Node = Node>> ConstLoader<ValueHandle<H::Node>> for ConstFoldContext<'_, H> {
+impl<H: HugrView> ConstLoader<ValueHandle<H::Node>> for ConstFoldContext<'_, H> {
     type Node = H::Node;
 
     fn value_from_opaque(
@@ -238,17 +228,7 @@ impl<H: HugrView<Node = Node>> ConstLoader<ValueHandle<H::Node>> for ConstFoldCo
         node: H::Node,
         type_args: &[TypeArg],
     ) -> Option<ValueHandle<H::Node>> {
-        if !type_args.is_empty() {
-            // TODO: substitution across Hugr (https://github.com/CQCL/hugr/issues/709)
-            return None;
-        };
-        // Returning the function body as a value, here, would be sufficient for inlining IndirectCall
-        // but not for transforming to a direct Call.
-        let func = DescendantsGraph::<FuncID<true>>::try_new(&**self, node).ok()?;
-        Some(ValueHandle::new_const_hugr(
-            ConstLocation::Node(node),
-            Box::new(func.extract_hugr()),
-        ))
+        Some(ValueHandle::NodeRef(node, type_args.to_vec()))
     }
 }
 
@@ -278,6 +258,51 @@ impl<H: HugrView<Node = Node>> DFContext<ValueHandle<H::Node>> for ConstFoldCont
                 partial_from_const(self, ConstLocation::Field(p.index(), &node.into()), &v);
         }
     }
+
+    fn interpret_call_indirect(
+        &mut self,
+        func: &PartialValue<ValueHandle<H::Node>>,
+        args: &[PartialValue<ValueHandle<H::Node>>],
+        outs: &mut [PartialValue<ValueHandle<H::Node>>],
+    ) {
+        let PartialValue::Value(func) = func else {
+            return;
+        };
+        let inputs = args.iter().cloned().enumerate().map(|(i, v)| (i.into(), v));
+        let vals: Vec<_> = match func {
+            ValueHandle::NodeRef(node, _) => {
+                let mut m = Machine::new(self.0);
+                m.prepopulate_inputs(*node, inputs).unwrap();
+                let results = m.run(ConstFoldContext(self.0), []);
+                (0..outs.len())
+                    .map(|p| results.read_out_wire(Wire::new(*node, p)))
+                    .collect()
+            }
+            ValueHandle::Unhashable {
+                leaf: Either::Right(hugr),
+                ..
+            } => {
+                let h = hugr.as_ref();
+                // The problem here---which we'd see if we didn't constrain H::Node==Node,
+                // because the ValueHandle's would be incompatible---is that `args` may contain
+                //   (a) UnhashableConsts keyed by NodeId in the *outer* Hugr (`self.0`, not `h`).
+                //   (b) NodeRefs referring to nodes in the outer Hugr !
+                //
+                // We can solve the first by remapping keys of HashedConsts to the input ports
+                // (like `fresh_node` in ConstFoldContext::run_no_validate), but not the second.
+                let results = Machine::new(h).run(ConstFoldContext(h), inputs);
+                (0..outs.len())
+                    .map(|p| results.read_out_wire(Wire::new(h.root(), p)))
+                    .collect()
+            }
+            _ => return,
+        };
+        for (val, out) in vals.into_iter().zip_eq(outs) {
+            if let Some(val) = val {
+                *out = val;
+            }
+        }
+    }
 }
 
 #[cfg(test)]
diff --git a/hugr-passes/src/const_fold/value_handle.rs b/hugr-passes/src/const_fold/value_handle.rs
index bda7bffd2..441b88788 100644
--- a/hugr-passes/src/const_fold/value_handle.rs
+++ b/hugr-passes/src/const_fold/value_handle.rs
@@ -7,6 +7,7 @@ use std::sync::Arc;
 use hugr_core::core::HugrNode;
 use hugr_core::ops::constant::OpaqueValue;
 use hugr_core::ops::Value;
+use hugr_core::types::TypeArg;
 use hugr_core::{Hugr, Node};
 use itertools::Either;
 
@@ -46,6 +47,15 @@ impl Hash for HashedConst {
 /// An [Eq]-able and [Hash]-able leaf (non-[Sum](Value::Sum)) Value
 #[derive(Clone, Debug)]
 pub enum ValueHandle<N = Node> {
+    /// The result of [LoadFunction] on a [FuncDefn] (or [FuncDecl]), i.e. a "function
+    /// pointer" to a function in the Hugr. (Cannot be represented as a [Value::Function]
+    /// without lots of cloning, because it may have static edges from other
+    /// functions/constants/etc.)
+    ///
+    /// [LoadFunction]: hugr_core::ops::LoadFunction
+    /// [FuncDefn]: hugr_core::ops::FuncDefn
+    /// [FuncDecl]: hugr_core::ops::FuncDefn
+    NodeRef(N, Vec<TypeArg>),
     /// A [Value::Extension] that has been hashed
     Hashable(HashedConst),
     /// Either a [Value::Extension] that can't be hashed, or a [Value::Function].
@@ -108,6 +118,7 @@ impl<N: HugrNode> AbstractValue for ValueHandle<N> {}
 impl<N: HugrNode> PartialEq for ValueHandle<N> {
     fn eq(&self, other: &Self) -> bool {
         match (self, other) {
+            (Self::NodeRef(n1, args1), Self::NodeRef(n2, args2)) => n1 == n2 && args1 == args2,
             (Self::Hashable(h1), Self::Hashable(h2)) => h1 == h2,
             (
                 Self::Unhashable {
@@ -138,6 +149,10 @@ impl<N: HugrNode> Eq for ValueHandle<N> {}
 impl<N: HugrNode> Hash for ValueHandle<N> {
     fn hash<I: Hasher>(&self, state: &mut I) {
         match self {
+            ValueHandle::NodeRef(n, args) => {
+                n.hash(state);
+                args.hash(state);
+            }
             ValueHandle::Hashable(hc) => hc.hash(state),
             ValueHandle::Unhashable {
                 node,
@@ -153,9 +168,11 @@ impl<N: HugrNode> Hash for ValueHandle<N> {
 
 // Unfortunately we need From<ValueHandle> for Value to be able to pass
 // Value's into interpret_leaf_op. So that probably doesn't make sense...
-impl<N: HugrNode> From<ValueHandle<N>> for Value {
-    fn from(value: ValueHandle<N>) -> Self {
-        match value {
+impl<N: HugrNode> TryFrom<ValueHandle<N>> for Value {
+    type Error = N;
+    fn try_from(value: ValueHandle<N>) -> Result<Value, N> {
+        Ok(match value {
+            ValueHandle::NodeRef(n, _) => return Err(n),
             ValueHandle::Hashable(HashedConst { val, .. })
             | ValueHandle::Unhashable {
                 leaf: Either::Left(val),
@@ -169,7 +186,7 @@ impl<N: HugrNode> From<ValueHandle<N>> for Value {
             } => Value::function(Arc::try_unwrap(hugr).unwrap_or_else(|a| a.as_ref().clone()))
                 .map_err(|e| e.to_string())
                 .unwrap(),
-        }
+        })
     }
 }
 
diff --git a/hugr-passes/src/dataflow.rs b/hugr-passes/src/dataflow.rs
index 43caa9c94..6db55b92b 100644
--- a/hugr-passes/src/dataflow.rs
+++ b/hugr-passes/src/dataflow.rs
@@ -35,6 +35,18 @@ pub trait DFContext<V>: ConstLoader<V> {
         _outs: &mut [PartialValue<V>],
     ) {
     }
+
+    /// Given lattice values for the called function, and arguments to pass to it, update
+    /// lattice values for the (dataflow) outputs
+    /// of a [CallIndirect](hugr_core::ops::CallIndirect).
+    /// (The default does nothing, i.e. leaves `Top` for all outputs.)
+    fn interpret_call_indirect(
+        &mut self,
+        _func: &PartialValue<V>,
+        _args: &[PartialValue<V>],
+        _outs: &mut [PartialValue<V>],
+    ) {
+    }
 }
 
 /// A location where a [Value] could be find in a Hugr. That is,
diff --git a/hugr-passes/src/dataflow/datalog.rs b/hugr-passes/src/dataflow/datalog.rs
index 13e510daf..037ca2bda 100644
--- a/hugr-passes/src/dataflow/datalog.rs
+++ b/hugr-passes/src/dataflow/datalog.rs
@@ -401,6 +401,13 @@ fn propagate_leaf_op<V: AbstractValue, H: HugrView>(
                 outs
             }))
         }
-        o => todo!("Unhandled: {:?}", o), // At least CallIndirect, and OpType is "non-exhaustive"
+        OpType::CallIndirect(_) => Some(ValueRow::from_iter(if row_contains_bottom(ins) {
+            vec![PartialValue::Bottom; num_outs]
+        } else {
+            let mut outs = vec![PartialValue::Top; num_outs];
+            ctx.interpret_call_indirect(&ins[0], &ins[1..], &mut outs[..]);
+            outs
+        })),
+        o => todo!("Unhandled: {:?}", o), // OpType is "non-exhaustive"
     }
 }