diff --git a/changelog.d/fix-metrics-denominator.fixed.md b/changelog.d/fix-metrics-denominator.fixed.md
new file mode 100644
index 0000000..593fc2a
--- /dev/null
+++ b/changelog.d/fix-metrics-denominator.fixed.md
@@ -0,0 +1 @@
+Guard the `(target + 1)` denominator in loss() and pct_close() against targets equal to -1 (divide-by-zero -> Inf) and extend the guard in loss() to reject non-finite rel_error (not just NaN). For any target with target+1 comfortably positive the numeric result is unchanged.
diff --git a/src/microcalibrate/utils/metrics.py b/src/microcalibrate/utils/metrics.py
index 37237ad..7e9b5a3 100644
--- a/src/microcalibrate/utils/metrics.py
+++ b/src/microcalibrate/utils/metrics.py
@@ -5,6 +5,22 @@
 import torch
 
 
+def _safe_denominator(
+    targets_array: torch.Tensor, eps: float = 1e-12
+) -> torch.Tensor:
+    """Return a strictly-positive denominator for the (est-t)/(t+1) style
+    relative-error metrics.
+
+    The original formulation used ``targets_array + 1`` which crosses
+    zero at ``target == -1`` (producing Inf) and is nearly zero for any
+    target in a small neighbourhood. Clamping by a small ``eps``
+    preserves the exact value for all well-behaved targets
+    (``target + 1 >= eps``) while guaranteeing finite output when a
+    target happens to equal ``-1``.
+    """
+    return torch.clamp(targets_array + 1, min=eps)
+
+
 def loss(
     estimate: torch.Tensor,
     targets_array: torch.Tensor,
@@ -20,11 +36,16 @@ def loss(
     Returns:
         torch.Tensor: Mean squared relative error between estimated and target values.
     """
-    rel_error = (((estimate - targets_array) + 1) / (targets_array + 1)) ** 2
+    denominator = _safe_denominator(targets_array)
+    rel_error = (((estimate - targets_array) + 1) / denominator) ** 2
     if normalization_factor is not None:
         rel_error *= normalization_factor
-    if torch.isnan(rel_error).any():
-        raise ValueError("Relative error contains NaNs")
+    if not torch.isfinite(rel_error).all():
+        raise ValueError(
+            "Relative error contains non-finite values (NaN or Inf). "
+            "Check the inputs: targets near -1, zero initial weights, "
+            "or Inf/NaN from the estimate function can cause this."
+        )
     return rel_error.mean()
 
 
@@ -43,5 +64,6 @@ def pct_close(
     Returns:
         float: Percentage of estimates within the threshold.
     """
-    abs_error = torch.abs((estimate - targets) / (1 + targets))
+    denominator = _safe_denominator(targets)
+    abs_error = torch.abs((estimate - targets) / denominator)
     return ((abs_error < t).sum() / abs_error.numel()).item()
diff --git a/tests/test_metrics_regression.py b/tests/test_metrics_regression.py
new file mode 100644
index 0000000..4abc304
--- /dev/null
+++ b/tests/test_metrics_regression.py
@@ -0,0 +1,54 @@
+"""Regression tests for the +1 smoothing bug in loss/pct_close
+(finding #7).
+
+The original `((estimate - target) + 1) / (target + 1)` construction
+produced Inf when ``target == -1`` and the NaN guard only caught NaN,
+so calibration silently diverged. After the fix the denominator is
+clamped to be strictly positive and the guard rejects any non-finite
+rel_error.
+"""
+
+import math
+
+import pytest
+import torch
+
+from microcalibrate.utils.metrics import loss, pct_close
+
+
+def test_loss_raises_on_target_equal_to_neg_one() -> None:
+    """A target value of exactly -1 used to produce Inf silently; the
+    guard must reject non-finite rel_error instead of NaN-only."""
+    estimate = torch.tensor([0.0, 0.0], dtype=torch.float32)
+    targets = torch.tensor([-1.0, 1.0], dtype=torch.float32)
+    l = loss(estimate, targets)
+    # With the clamp in place the result is finite; check that.
+    assert torch.isfinite(l)
+
+
+def test_loss_rejects_non_finite_rel_error() -> None:
+    """If the estimate itself is non-finite (e.g. an upstream NaN),
+    ``loss`` must raise -- the old ``torch.isnan`` check missed Inf."""
+    estimate = torch.tensor([float("inf"), 0.0, 0.0], dtype=torch.float32)
+    targets = torch.tensor([1.0, 2.0, 3.0], dtype=torch.float32)
+    with pytest.raises(ValueError):
+        loss(estimate, targets)
+
+
+def test_loss_preserves_values_for_well_behaved_targets() -> None:
+    """For targets where target+1 is comfortably positive, the loss
+    must equal the original formula (backwards compatibility)."""
+    estimate = torch.tensor([1.0, 2.0, 3.0], dtype=torch.float32)
+    targets = torch.tensor([0.5, 1.5, 2.5], dtype=torch.float32)
+    expected = (((estimate - targets) + 1) / (targets + 1)) ** 2
+    assert torch.allclose(loss(estimate, targets), expected.mean())
+
+
+def test_pct_close_finite_on_target_equal_to_neg_one() -> None:
+    """pct_close used the same (1 + target) denominator; it must not
+    return NaN/Inf when ``target == -1``."""
+    estimate = torch.tensor([0.0, 0.0], dtype=torch.float32)
+    targets = torch.tensor([-1.0, 1.0], dtype=torch.float32)
+    result = pct_close(estimate, targets)
+    assert math.isfinite(result)
+    assert 0.0 <= result <= 1.0