diff --git a/docs/tutorial.md b/docs/tutorial.md
index 041fdefe..fbba5aa4 100644
--- a/docs/tutorial.md
+++ b/docs/tutorial.md
@@ -92,7 +92,7 @@ plt.show()
 
 ### Select a Rank with Bi-Cross-Validation (BiCV)
 
-$R^2X$ (in-sample fit) always increases with rank, so it cannot by itself identify an optimal rank — it can only reveal an elbow. Bi-cross-validation (BiCV) addresses this by holding out a random subset of cells *and* genes, fitting RISE on the remaining data, and scoring how well the fit predicts the held-out block. Because it is evaluated on unseen data, BiCV $R^2X$ penalizes overfitting and typically peaks (or plateaus) near the rank that generalizes best, unlike the fit $R^2X$.
+$R^2X$ (in-sample fit) always increases with rank, so it cannot by itself identify an optimal rank. Bi-cross-validation (BiCV) addresses this by holding out a random subset of cells *and* genes, fitting RISE on the remaining data, and scoring how well the fit predicts the held-out block. Because it is evaluated on unseen data, BiCV $R^2X$ penalizes overfitting and turns over near the rank that generalizes best, unlike the fit $R^2X$. 
 
 `scrise.rank_selection.bicv` exhaustively evaluates a list of candidate ranks, each with several repeated random train/test splits, and returns both the fit $R^2X$ and the BiCV $R^2X$ for every rank so you can inspect the full curve. Since PARAFAC2 fits use CANDELINC compression by default (`compress="auto"`), sweeping every rank in this way is cheap enough that there is no need to search for the best rank without evaluating every candidate.
 
@@ -110,7 +110,7 @@ plt.tight_layout()
 plt.show()
 ```
 
-`bicv` returns a long-form DataFrame (columns `Rank`, `Repeat`, `Metric`, `R2X`, plus the per-trial diagnostics below) suitable for further analysis as well as plotting. Each BiCV trial holds out `held_out_cell_frac` of the cells within each condition and `held_out_gene_frac` of the genes (both default to 0.2); increase `n_repeats` for a smoother, less noisy BiCV curve at the cost of more compute.
+`bicv` returns a long-form DataFrame (columns `Rank`, `Repeat`, `Metric`, `R2X`, plus the per-trial diagnostics below) suitable for further analysis as well as plotting. Each BiCV trial holds out `held_out_cell_frac` of the cells within each condition and `held_out_gene_frac` of the genes. Both default to 0.5, the half-rows-and-half-columns split recommended by [Owen and Perry](https://arxiv.org/abs/0908.2062), who report that "in simulated examples we find that a method leaving out half the rows and half the columns performs well". Increase `n_repeats` for a smoother, less noisy BiCV curve at the cost of more compute.
 
 Each BiCV row also carries the diagnostics needed to audit the curve rather than just plot it:
 
diff --git a/scrise/rank_selection.py b/scrise/rank_selection.py
index f928d284..89d77f74 100644
--- a/scrise/rank_selection.py
+++ b/scrise/rank_selection.py
@@ -88,6 +88,19 @@ def _cell_loadings(
     return Z
 
 
+def _holdout_scale(
+    cond_train: np.ndarray, cond_test: np.ndarray, n_cond: int
+) -> np.ndarray:
+    """Per-held-out-cell factor correcting `A` for the held-out slice's size."""
+    scale = np.ones(cond_test.size)
+    train_counts = np.bincount(cond_train, minlength=n_cond)
+    test_counts = np.bincount(cond_test, minlength=n_cond)
+    for i in range(n_cond):
+        if test_counts[i] and train_counts[i]:
+            scale[cond_test == i] = np.sqrt(test_counts[i] / train_counts[i])
+    return scale[:, np.newaxis]
+
+
 # Nonzeros per row block when streaming column moments. Bounds the per-nonzero
 # temporaries to a few hundred MB regardless of how large the matrix is.
 _MOMENT_CHUNK_NNZ = 50_000_000
@@ -231,8 +244,10 @@ def _bicv_trial(
     cond_slices_test = condition_slices(cond_test, n_cond)
     P_test, _ = project_data(W_test, [A, B, C], cond_slices_test)
 
-    # Score the held-out block.
+    # Score the held-out block. `A` carries the training slice's energy, so the
+    # held-out loadings need rescaling for the held-out slice's size.
     L = _cell_loadings(P_test, B, A, cond_test, n_cond)
+    L *= _holdout_scale(cond_train, cond_test, n_cond)
     LtY = np.asarray(
         rmatmul(np.ascontiguousarray(L.T), X_mat[test_cell_mask]), dtype=np.float64
     )[:, test_gene_idx]
@@ -266,8 +281,8 @@ def bicv(
     X: anndata.AnnData | None = None,
     ranks: Sequence[int] | None = None,
     n_repeats: int = 3,
-    held_out_cell_frac: float = 0.2,
-    held_out_gene_frac: float = 0.2,
+    held_out_cell_frac: float = 0.5,
+    held_out_gene_frac: float = 0.5,
     random_state: int | None = None,
     tolerance: float = 1e-6,
     max_iter: int = 200,
@@ -298,9 +313,9 @@ def bicv(
     n_repeats : int, optional (default: 3)
         Number of independent random cell/gene splits per rank. Higher
         values give a less noisy BiCV estimate but take longer.
-    held_out_cell_frac : float, optional (default: 0.2)
+    held_out_cell_frac : float, optional (default: 0.5)
         Fraction of cells held out per condition in each BiCV trial.
-    held_out_gene_frac : float, optional (default: 0.2)
+    held_out_gene_frac : float, optional (default: 0.5)
         Fraction of genes held out in each BiCV trial.
     random_state : int, optional
         Random seed for reproducibility.
diff --git a/scrise/tests/test_rank_selection.py b/scrise/tests/test_rank_selection.py
index 960f1c30..3155ea59 100644
--- a/scrise/tests/test_rank_selection.py
+++ b/scrise/tests/test_rank_selection.py
@@ -13,6 +13,7 @@
 from ..rank_selection import (
     _bicv_trial,
     _cell_loadings,
+    _holdout_scale,
     _split_cells_by_condition,
     _split_genes,
     _test_block_moments,
@@ -325,8 +326,8 @@ def test_reported_seed_reproduces_its_own_trial():
     replayed = _bicv_trial(
         X,
         rank=3,
-        held_out_cell_frac=0.2,
-        held_out_gene_frac=0.2,
+        held_out_cell_frac=0.5,
+        held_out_gene_frac=0.5,
         seed=int(target["Seed"]),
         tolerance=1e-6,
         max_iter=60,
@@ -388,8 +389,12 @@ def dense(mat):
         sel = cond_test == i
         if not np.any(sel):
             continue
+        n_train_i = int(np.sum(cond_train == i))
+        # `A[i]` carries the training slice's energy; rescale it for this
+        # slice's size (see `_holdout_scale`).
+        scale = np.sqrt(int(sel.sum()) / n_train_i) if n_train_i else 1.0
         actual = X_test_test[sel]
-        recon = ((P_test[i] @ B) * A[i]) @ C_test.T
+        recon = (((P_test[i] @ B) * A[i]) * scale) @ C_test.T
         ss_res += float(np.sum((actual - recon) ** 2))
         ss_tot += float(np.sum(actual**2))
     return 1.0 - ss_res / ss_tot
@@ -500,3 +505,119 @@ def test_block_moments_stream_across_more_than_one_row_block(monkeypatch):
     block = dense[cell_mask]
     np.testing.assert_allclose(sums, block.sum(axis=0), rtol=1e-12)
     np.testing.assert_allclose(squares, np.sum(block**2, axis=0), rtol=1e-12)
+
+
+# Held-out slice scaling
+
+
+def _exact_low_rank(
+    rank_true=4, noise=0.0, n_cond=6, cells=(90, 160), n_genes=90, seed=0
+):
+    """Data that IS exactly rank `rank_true`, with unequal cells per condition.
+
+    `means` is zero so the target stays exactly low rank -- mean-centering
+    would add a rank-one term and put a ceiling below 1.0 on the fit.
+    """
+    rng = np.random.default_rng(seed)
+    C = rng.normal(size=(n_genes, rank_true))
+    B = rng.normal(size=(rank_true, rank_true))
+    A = np.abs(rng.normal(size=(n_cond, rank_true))) + 1.0
+    blocks, cond = [], []
+    for k in range(n_cond):
+        n_k = int(rng.integers(*cells))
+        P, _ = np.linalg.qr(rng.normal(size=(n_k, rank_true)))
+        blocks.append(((P @ B) * A[k]) @ C.T)
+        cond.append(np.full(n_k, k))
+    mat = np.concatenate(blocks, axis=0)
+    if noise:
+        mat = mat + noise * np.std(mat) * rng.normal(size=mat.shape)
+    adata = anndata.AnnData(X=mat)
+    adata.obs["condition_unique_idxs"] = np.concatenate(cond)
+    adata.var["means"] = np.zeros(n_genes)
+    return adata
+
+
+def test_holdout_scale_is_the_square_root_of_the_cell_count_ratio():
+    cond_train = np.repeat([0, 1, 2], [80, 40, 10])
+    cond_test = np.repeat([0, 1, 2], [20, 40, 90])
+
+    scale = _holdout_scale(cond_train, cond_test, 3)
+
+    assert scale.shape == (cond_test.size, 1)
+    np.testing.assert_allclose(scale[cond_test == 0, 0], np.sqrt(20 / 80))
+    np.testing.assert_allclose(scale[cond_test == 1, 0], np.sqrt(40 / 40))
+    np.testing.assert_allclose(scale[cond_test == 2, 0], np.sqrt(90 / 10))
+
+
+def test_holdout_scale_is_one_for_an_even_split():
+    """The split the defaults use, and the only one that needed no correction."""
+    cond_train = np.repeat([0, 1], [50, 30])
+    cond_test = np.repeat([0, 1], [50, 30])
+    np.testing.assert_allclose(_holdout_scale(cond_train, cond_test, 2), 1.0)
+
+
+def test_holdout_scale_leaves_conditions_it_cannot_compare_alone():
+    """A condition absent from either side keeps a factor of one."""
+    cond_train = np.array([0, 0, 0])
+    cond_test = np.array([0, 2, 2])
+    scale = _holdout_scale(cond_train, cond_test, 3)
+    np.testing.assert_allclose(scale[cond_test == 2, 0], 1.0)
+
+
+def test_exactly_low_rank_data_scores_near_one_at_its_own_rank():
+    """The regression that matters: in-sample ~1 must not come with held-out < 0.
+
+    Before the slice-size correction this returned about -0.03 while the
+    training block scored 0.9996 -- the model recovered the structure and the
+    held-out score still said it was worse than predicting the mean.
+    """
+    adata = _exact_low_rank(rank_true=4)
+    trial = _bicv_trial(adata, 4, 0.5, 0.5, seed=0, tolerance=1e-8, max_iter=300)
+
+    assert trial["Train Block R2X"] > 0.99
+    assert trial["BiCV R2X"] > 0.95
+
+
+@pytest.mark.parametrize("frac", [0.2, 0.35, 0.5, 0.7])
+def test_score_barely_moves_with_the_held_out_fraction(frac):
+    """`held_out_cell_frac` sets how much is held out, not what the score is.
+
+    The bug made this swing from -2.85 (frac 0.1) to 0.90 (frac 0.5) on the
+    same data at the same rank, because the error was sqrt(n_train/n_test).
+    """
+    adata = _exact_low_rank(rank_true=4)
+    trial = _bicv_trial(adata, 4, frac, frac, seed=0, tolerance=1e-8, max_iter=300)
+    assert trial["BiCV R2X"] > 0.9
+
+
+def test_bicv_recovers_a_known_rank():
+    """The point of the metric: peak (or plateau onset) at the true rank."""
+    adata = _exact_low_rank(rank_true=3, noise=0.5, n_genes=60)
+    results = bicv(adata, [1, 2, 3, 5, 8], n_repeats=2, random_state=0, max_iter=150)
+    means = results[results["Metric"] == "BiCV R2X"].groupby("Rank")["R2X"].mean()
+
+    # Climbs up to the true rank, then stops climbing.
+    assert means.loc[3] > means.loc[2] > means.loc[1]
+    assert means.loc[5] <= means.loc[3] + 1e-3
+    assert means.loc[8] <= means.loc[3] + 1e-3
+
+
+def test_pure_noise_does_not_score_positive():
+    """Nothing generalises from noise; a positive score would mean leakage."""
+    rng = np.random.default_rng(0)
+    cond = np.repeat(np.arange(5), 70)
+    adata = anndata.AnnData(X=rng.normal(size=(cond.size, 60)))
+    adata.obs["condition_unique_idxs"] = cond
+    adata.var["means"] = np.zeros(60)
+
+    trial = _bicv_trial(adata, 5, 0.5, 0.5, seed=0, tolerance=1e-8, max_iter=200)
+    assert trial["BiCV R2X"] < 0.02
+
+
+def test_held_out_fractions_default_to_one_half():
+    """Owen and Perry's recommended split; see the module docstring."""
+    import inspect
+
+    params = inspect.signature(bicv).parameters
+    assert params["held_out_cell_frac"].default == 0.5
+    assert params["held_out_gene_frac"].default == 0.5