diff --git a/CHANGELOG.md b/CHANGELOG.md
index 170f0530..413d3c4f 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -18,6 +18,10 @@ changelog does not include internal changes that do not affect the user.
   matrix are almost equal. Rounding errors could make the squared distance between such rows
   slightly negative, giving a `nan` distance that was then ignored when computing the scores.
   Squared distances are now clamped to be non-negative before taking the square root.
+- Fixed `AlignedMTL` and `AlignedMTLWeighting` ignoring tasks with a much smaller gradient than
+  the others when the input is in `float64`. The tolerance used to find the rank of the Gramian was
+  always based on the machine epsilon of the default dtype (usually `float32`) instead of the dtype
+  of the Gramian, so valid small eigenvalues were discarded.
 - Fixed `Engine.compute_gramian` silently ignoring the contribution of a module when one of its
   forward passes had no associated backward pass (e.g. because its output was detached). It now
   raises a `ValueError` instead.
diff --git a/src/torchjd/aggregation/_aligned_mtl.py b/src/torchjd/aggregation/_aligned_mtl.py
index 5cb389c0..7df1558c 100644
--- a/src/torchjd/aggregation/_aligned_mtl.py
+++ b/src/torchjd/aggregation/_aligned_mtl.py
@@ -61,7 +61,7 @@ def _compute_balance_transformation(
         scale_mode: SUPPORTED_SCALE_MODE = "min",
     ) -> Tensor:
         lambda_, V = torch.linalg.eigh(M, UPLO="U")  # More modern equivalent to torch.symeig
-        tol = torch.max(lambda_) * len(M) * torch.finfo().eps
+        tol = torch.max(lambda_) * len(M) * torch.finfo(M.dtype).eps
         rank = sum(lambda_ > tol)
 
         if rank == 0:
diff --git a/tests/unit/aggregation/test_aligned_mtl.py b/tests/unit/aggregation/test_aligned_mtl.py
index 6eacfba9..3608a3ea 100644
--- a/tests/unit/aggregation/test_aligned_mtl.py
+++ b/tests/unit/aggregation/test_aligned_mtl.py
@@ -1,7 +1,8 @@
 import torch
 from pytest import mark, raises
 from torch import Tensor
-from utils.tensors import ones_
+from torch.testing import assert_close
+from utils.tensors import ones_, tensor_
 
 from torchjd.aggregation import AlignedMTL, ConstantWeighting
 
@@ -59,3 +60,9 @@ def test_scale_mode_setter_updates_value() -> None:
     A.scale_mode = "rmse"
     assert A.scale_mode == "rmse"
     assert A.gramian_weighting.scale_mode == "rmse"
+
+
+def test_float64_small_eigenvalue_is_kept() -> None:
+    J = tensor_([[1.0, 0.0], [0.0, 1e-4]], dtype=torch.float64)
+    result = AlignedMTL()(J)
+    assert_close(result, tensor_([5e-5, 5e-5], dtype=torch.float64))