diff --git a/docs/CHANGELOG.md b/docs/CHANGELOG.md
index ca9fe8f35..859ca9929 100644
--- a/docs/CHANGELOG.md
+++ b/docs/CHANGELOG.md
@@ -13,6 +13,7 @@
 * `rugnux` reports twinning measured before and after the space group was decided, and no longer reports it when the L-test contradicts it.
 * `rugnux --mode calibration` writes `<prefix>.json` beside the `.poni`, holding the geometry as a `jfjoch_broker` `dataset_settings` body.
 * `rugnux --no-refine-tilt` holds the detector tilt at the value in the file instead of zeroing it.
+* `rugnux` refines only the detector-tilt component the data determine, holding the one along the rotation axis, so a beam-centre error is no longer reported as a tilt.
 * `jfjoch_writer` writes `direct_beam_x`/`direct_beam_y` in the HDF5 master - where the undeflected beam lands - beside the `beam_center_x`/`beam_center_y` PONI.
 * `jfjoch_broker` sends `direct_beam_x`/`direct_beam_y` on the CBOR start message.
 * `jfjoch_viewer` reads PILATUS miniCBF sweeps natively, and draws grid scan cells in the proportion of the scan steps.
diff --git a/image_analysis/geom_refinement/XtalOptimizer.cpp b/image_analysis/geom_refinement/XtalOptimizer.cpp
index a04251122..58c357762 100644
--- a/image_analysis/geom_refinement/XtalOptimizer.cpp
+++ b/image_analysis/geom_refinement/XtalOptimizer.cpp
@@ -365,14 +365,23 @@ bool XtalOptimizerInternal(XtalOptimizerData &data,
         // as the data's does, so the split it picks between two aliased parameters is the same however
         // much data the stage has. More frames, a longer sweep or a later stage cannot break it.
         constexpr double sigma_px = 3.0;
-        // The tilt's own budget, in the same direct-beam pixels. It is TIGHTER than the beam's on
-        // purpose: the data determine the sum of the two, so with equal budgets the shift splits
-        // evenly and half of a beam-centre error still arrives as an angle (measured: the coupling to
-        // the starting beam centre falls only from 79% to 41% of one-for-one at equal budgets). The
-        // detector tilt is a property of the mounting, re-measured when the detector is calibrated;
-        // the beam centre drifts between runs. When both ends of an alias have to be restrained, the
-        // tighter restraint belongs on the one that moves less.
-        constexpr double SIGMA_TILT_PX = 1.0;
+        // The tilt's budgets, in those same direct-beam pixels: one for the spindle-parallel
+        // combination and one for the perpendicular one. Zero means no restraint at all, so which
+        // component is held and which is refined is these two numbers and nothing else.
+        //
+        // The parallel one is TIGHTER than the beam's on purpose: the data determine the SUM of the
+        // two, so with equal budgets the shift splits evenly and half of a beam-centre error still
+        // arrives as an angle (measured: the coupling to the starting beam centre falls only from
+        // 79% to 41% of one-for-one at equal budgets, and to 8% at this one). The detector tilt is a
+        // property of the mounting, re-measured when the detector is calibrated; the beam centre
+        // drifts between runs. When both ends of an alias have to be restrained, the tighter
+        // restraint belongs on the one that moves less.
+        //
+        // The perpendicular one is free. That is the arrangement the data support today: it is the
+        // component whose conditioning tracks the 2theta the fit reaches, i.e. the one the data speak
+        // about, while the parallel one's does not move with 2theta at all.
+        constexpr double SIGMA_TILT_PARALLEL_PX = 1.0;
+        constexpr double SIGMA_TILT_PERPENDICULAR_PX = 0.0;
         const double gauge_w = data.geom.GetPixelSize_mm() / (distance_mm * data.geom.GetWavelength_A())
                                * std::sqrt(effective_spots) / sigma_px;
 
@@ -424,15 +433,24 @@ bool XtalOptimizerInternal(XtalOptimizerData &data,
                 // has no such compensator, and whether the parallel component is measurable there is a
                 // different question with a different answer. This restraint is local to the fit that
                 // co-refines the orientation and does not speak for any other.
-                if (data.axis)
-                    problem.AddResidualBlock(
-                        new ceres::AutoDiffCostFunction<GaugeDirectionPrior, 1, 2>(
-                            new GaugeDirectionPrior(gauge_rot_x, gauge_rot_y,
-                                                    gauge_rot_x * detector_rot[0]
-                                                        + gauge_rot_y * detector_rot[1],
-                                                    gauge_w * (sigma_px / SIGMA_TILT_PX)
-                                                        * distance_mm / data.geom.GetPixelSize_mm())),
-                        nullptr, detector_rot);
+                if (data.axis) {
+                    const double lever = distance_mm / data.geom.GetPixelSize_mm();
+                    // Parallel first, then the perpendicular direction (-gy, gx). Both go through the
+                    // same restraint, so swapping which one is held is a change to the two budgets.
+                    const double dirs[2][2] = {{gauge_rot_x, gauge_rot_y}, {-gauge_rot_y, gauge_rot_x}};
+                    const double budget[2] = {SIGMA_TILT_PARALLEL_PX, SIGMA_TILT_PERPENDICULAR_PX};
+                    for (int i = 0; i < 2; ++i) {
+                        if (budget[i] <= 0.0)
+                            continue;
+                        problem.AddResidualBlock(
+                            new ceres::AutoDiffCostFunction<GaugeDirectionPrior, 1, 2>(
+                                new GaugeDirectionPrior(dirs[i][0], dirs[i][1],
+                                                        dirs[i][0] * detector_rot[0]
+                                                            + dirs[i][1] * detector_rot[1],
+                                                        gauge_w * (sigma_px / budget[i]) * lever)),
+                            nullptr, detector_rot);
+                    }
+                }
             }
 
             if (!data.refine_rotation_axis) {