diff --git a/pineappl/src/grid.rs b/pineappl/src/grid.rs
index f526dbc2..bea927b4 100644
--- a/pineappl/src/grid.rs
+++ b/pineappl/src/grid.rs
@@ -4,6 +4,7 @@ use super::bin::{BinInfo, BinLimits, BinRemapper};
 use super::lagrange_subgrid::{LagrangeSparseSubgridV1, LagrangeSubgridV1, LagrangeSubgridV2};
 use super::lumi::LumiEntry;
 use super::ntuple_subgrid::NtupleSubgridV1;
+use super::read_only_sparse_subgrid::ReadOnlySparseSubgridV1;
 use super::subgrid::{ExtraSubgridParams, Subgrid, SubgridEnum, SubgridParams};
 use either::Either::{Left, Right};
 use float_cmp::approx_eq;
@@ -711,10 +712,17 @@ impl Grid {
                     let mut new_subgrid = LagrangeSparseSubgridV1::from(&*grid).into();
                     mem::swap(subgrid, &mut new_subgrid);
                 }
-                SubgridEnum::LagrangeSparseSubgridV1(_) => {
+                SubgridEnum::LagrangeSubgridV2(grid) => {
+                    let mut new_subgrid = ReadOnlySparseSubgridV1::from(&*grid).into();
+                    mem::swap(subgrid, &mut new_subgrid);
+                }
+                SubgridEnum::LagrangeSparseSubgridV1(_)
+                | SubgridEnum::ReadOnlySparseSubgridV1(_) => {
                     // nothing to optimize here
                 }
-                SubgridEnum::NtupleSubgridV1(_) | SubgridEnum::LagrangeSubgridV2(_) => todo!(),
+                SubgridEnum::NtupleSubgridV1(_) => {
+                    todo!()
+                }
             }
         }
     }
diff --git a/pineappl/src/lagrange_subgrid.rs b/pineappl/src/lagrange_subgrid.rs
index c705d7a9..b2ac386b 100644
--- a/pineappl/src/lagrange_subgrid.rs
+++ b/pineappl/src/lagrange_subgrid.rs
@@ -10,7 +10,7 @@ use ndarray::Array3;
 use serde::{Deserialize, Serialize};
 use std::mem;
 
-fn weightfun(x: f64) -> f64 {
+pub(crate) fn weightfun(x: f64) -> f64 {
     (x.sqrt() / (1.0 - 0.99 * x)).powi(3)
 }
 
@@ -357,14 +357,14 @@ impl Subgrid for LagrangeSubgridV1 {
 /// Subgrid which uses Lagrange-interpolation.
 #[derive(Deserialize, Serialize)]
 pub struct LagrangeSubgridV2 {
-    grid: Option<Array3<f64>>,
-    ntau: usize,
-    ny1: usize,
-    ny2: usize,
+    pub(crate) grid: Option<Array3<f64>>,
+    pub(crate) ntau: usize,
+    pub(crate) ny1: usize,
+    pub(crate) ny2: usize,
     y1order: usize,
     y2order: usize,
     tauorder: usize,
-    itaumin: usize,
+    pub(crate) itaumin: usize,
     itaumax: usize,
     reweight1: bool,
     reweight2: bool,
@@ -374,7 +374,7 @@ pub struct LagrangeSubgridV2 {
     y2max: f64,
     taumin: f64,
     taumax: f64,
-    static_q2: f64,
+    pub(crate) static_q2: f64,
 }
 
 impl LagrangeSubgridV2 {
diff --git a/pineappl/src/lib.rs b/pineappl/src/lib.rs
index 745f2525..0154da19 100644
--- a/pineappl/src/lib.rs
+++ b/pineappl/src/lib.rs
@@ -11,5 +11,6 @@ pub mod grid;
 pub mod lagrange_subgrid;
 pub mod lumi;
 pub mod ntuple_subgrid;
+pub mod read_only_sparse_subgrid;
 pub mod sparse_array3;
 pub mod subgrid;
diff --git a/pineappl/src/read_only_sparse_subgrid.rs b/pineappl/src/read_only_sparse_subgrid.rs
new file mode 100644
index 00000000..bef4cece
--- /dev/null
+++ b/pineappl/src/read_only_sparse_subgrid.rs
@@ -0,0 +1,236 @@
+//! TODO
+
+use super::grid::Ntuple;
+use super::lagrange_subgrid::{self, LagrangeSubgridV2};
+use super::sparse_array3::SparseArray3;
+use super::subgrid::{ExtraSubgridParams, Subgrid, SubgridEnum, SubgridParams};
+use either::Either;
+use ndarray::Axis;
+use serde::{Deserialize, Serialize};
+use std::mem;
+
+/// TODO
+#[derive(Deserialize, Serialize)]
+pub struct ReadOnlySparseSubgridV1 {
+    array: SparseArray3<f64>,
+    q2_grid: Vec<f64>,
+    x1_grid: Vec<f64>,
+    x2_grid: Vec<f64>,
+    reweight_x1: Vec<f64>,
+    reweight_x2: Vec<f64>,
+}
+
+impl ReadOnlySparseSubgridV1 {
+    /// Constructor.
+    #[must_use]
+    pub fn new(
+        subgrid_params: &SubgridParams,
+        extra_subgrid_params: &ExtraSubgridParams,
+        q2_grid: Vec<f64>,
+        x1_grid: Vec<f64>,
+        x2_grid: Vec<f64>,
+        reweight_x1: Vec<f64>,
+        reweight_x2: Vec<f64>,
+    ) -> Self {
+        Self {
+            array: SparseArray3::new(
+                subgrid_params.q2_bins(),
+                subgrid_params.x_bins(),
+                extra_subgrid_params.x2_bins(),
+            ),
+            q2_grid,
+            x1_grid,
+            x2_grid,
+            reweight_x1,
+            reweight_x2,
+        }
+    }
+}
+
+impl Subgrid for ReadOnlySparseSubgridV1 {
+    fn convolute(
+        &self,
+        _: &[f64],
+        _: &[f64],
+        _: &[f64],
+        lumi: Either<&dyn Fn(usize, usize, usize) -> f64, &dyn Fn(f64, f64, f64) -> f64>,
+    ) -> f64 {
+        let lumi = lumi.left().unwrap();
+
+        self.array
+            .indexed_iter()
+            .map(|((iq2, ix1, ix2), sigma)| {
+                let mut value = sigma * lumi(ix1, ix2, iq2);
+                if !self.reweight_x1.is_empty() {
+                    value *= self.reweight_x1[ix1];
+                }
+                if !self.reweight_x2.is_empty() {
+                    value *= self.reweight_x2[ix2];
+                }
+                value
+            })
+            .sum()
+    }
+
+    fn fill(&mut self, _: &Ntuple<f64>) {
+        panic!("this grid doesn't support the fill operation");
+    }
+
+    fn q2_grid(&self) -> Vec<f64> {
+        self.q2_grid.clone()
+    }
+
+    fn x1_grid(&self) -> Vec<f64> {
+        self.x1_grid.clone()
+    }
+
+    fn x2_grid(&self) -> Vec<f64> {
+        self.x2_grid.clone()
+    }
+
+    fn is_empty(&self) -> bool {
+        self.array.is_empty()
+    }
+
+    fn merge(&mut self, other: &mut SubgridEnum, transpose: bool) {
+        if let SubgridEnum::ReadOnlySparseSubgridV1(other_grid) = other {
+            if self.array.is_empty() && !transpose {
+                mem::swap(&mut self.array, &mut other_grid.array);
+            } else {
+                // TODO: we need much more checks here if the subgrids are compatible at all
+
+                if transpose {
+                    for ((i, k, j), value) in other_grid.array.indexed_iter() {
+                        self.array[[i, j, k]] += value;
+                    }
+                } else {
+                    for ((i, j, k), value) in other_grid.array.indexed_iter() {
+                        self.array[[i, j, k]] += value;
+                    }
+                }
+            }
+        } else {
+            todo!();
+        }
+    }
+
+    fn scale(&mut self, factor: f64) {
+        if factor == 0.0 {
+            self.array.clear();
+        } else {
+            self.array.iter_mut().for_each(|x| *x *= factor);
+        }
+    }
+
+    fn q2_slice(&self) -> (usize, usize) {
+        let range = self.array.x_range();
+
+        (range.start, range.end)
+    }
+
+    fn fill_q2_slice(&self, q2_slice: usize, grid: &mut [f64]) {
+        let x1: Vec<_> = self
+            .x1_grid
+            .iter()
+            .enumerate()
+            .map(|(i, &x)| if self.reweight_x1.is_empty() { 1.0 } else { self.reweight_x1[i] } / x)
+            .collect();
+        let x2: Vec<_> = self
+            .x2_grid
+            .iter()
+            .enumerate()
+            .map(|(i, &x)| if self.reweight_x2.is_empty() { 1.0 } else { self.reweight_x2[i] } / x)
+            .collect();
+
+        for value in grid.iter_mut() {
+            *value = 0.0;
+        }
+
+        for ((_, ix1, ix2), value) in self
+            .array
+            .indexed_iter()
+            .filter(|((iq2, _, _), _)| *iq2 == q2_slice)
+        {
+            grid[ix1 * self.x2_grid.len() + ix2] = value * x1[ix1] * x2[ix2];
+        }
+    }
+
+    fn write_q2_slice(&mut self, q2_slice: usize, grid: &[f64]) {
+        self.array.remove_x(q2_slice);
+
+        grid.iter()
+            .enumerate()
+            .filter(|(_, &value)| value != 0.0)
+            .for_each(|(index, &value)| {
+                self.array[[
+                    q2_slice,
+                    index / self.x2_grid.len(),
+                    index % self.x2_grid.len(),
+                ]] = value;
+            });
+    }
+
+    fn symmetrize(&mut self) {
+        let mut new_array =
+            SparseArray3::new(self.q2_grid.len(), self.x1_grid.len(), self.x2_grid.len());
+
+        for ((i, j, k), &sigma) in self.array.indexed_iter().filter(|((_, j, k), _)| k > j) {
+            new_array[[i, j, k]] = sigma;
+        }
+        // do not change the diagonal entries (k==j)
+        for ((i, j, k), &sigma) in self.array.indexed_iter().filter(|((_, j, k), _)| k < j) {
+            new_array[[i, k, j]] += sigma;
+        }
+
+        mem::swap(&mut self.array, &mut new_array);
+    }
+}
+
+impl From<&LagrangeSubgridV2> for ReadOnlySparseSubgridV1 {
+    fn from(subgrid: &LagrangeSubgridV2) -> Self {
+        let array = subgrid.grid.as_ref().map_or_else(
+            || SparseArray3::new(subgrid.ntau, subgrid.ny1, subgrid.ny2),
+            // in the following case we should optimize when ny2 > ny1
+            |grid| {
+                if subgrid.static_q2 == -1.0 {
+                    SparseArray3::from_ndarray(grid, subgrid.itaumin, subgrid.ntau)
+                } else {
+                    // in this case we've detected a static scale for this bin and we can collapse
+                    // the Q^2 axis into a single bin
+                    SparseArray3::from_ndarray(
+                        &grid
+                            .sum_axis(Axis(0))
+                            .into_shape((1, subgrid.ny1, subgrid.ny2))
+                            .unwrap(),
+                        0,
+                        1,
+                    )
+                }
+            },
+        );
+        let q2_grid = if subgrid.static_q2 == -1.0 {
+            subgrid.q2_grid()
+        } else {
+            vec![subgrid.static_q2]
+        };
+        let x1_grid = subgrid.x1_grid();
+        let x2_grid = subgrid.x2_grid();
+        let reweight_x1 = x1_grid
+            .iter()
+            .map(|x| lagrange_subgrid::weightfun(*x))
+            .collect();
+        let reweight_x2 = x2_grid
+            .iter()
+            .map(|x| lagrange_subgrid::weightfun(*x))
+            .collect();
+
+        Self {
+            array,
+            q2_grid,
+            x1_grid,
+            x2_grid,
+            reweight_x1,
+            reweight_x2,
+        }
+    }
+}
diff --git a/pineappl/src/subgrid.rs b/pineappl/src/subgrid.rs
index e183302f..d443f2e9 100644
--- a/pineappl/src/subgrid.rs
+++ b/pineappl/src/subgrid.rs
@@ -3,6 +3,7 @@
 use super::grid::Ntuple;
 use super::lagrange_subgrid::{LagrangeSparseSubgridV1, LagrangeSubgridV1, LagrangeSubgridV2};
 use super::ntuple_subgrid::NtupleSubgridV1;
+use super::read_only_sparse_subgrid::ReadOnlySparseSubgridV1;
 use either::Either;
 use enum_dispatch::enum_dispatch;
 use serde::{Deserialize, Serialize};
@@ -20,6 +21,8 @@ pub enum SubgridEnum {
     LagrangeSparseSubgridV1,
     /// Lagrange-interpolation subgrid with possibly different x1 and x2 bins.
     LagrangeSubgridV2,
+    /// Read-only sparse subgrid with possibly different x1 and x2 bins.
+    ReadOnlySparseSubgridV1,
 }
 
 /// Trait each subgrid must implement.