diff --git a/napari/_qt/layers/qt_image_base_layer.py b/napari/_qt/layers/qt_image_base_layer.py
index 6a728b4f172..b0ea742e6bc 100644
--- a/napari/_qt/layers/qt_image_base_layer.py
+++ b/napari/_qt/layers/qt_image_base_layer.py
@@ -153,11 +153,21 @@ def create_range_popup(layer, attr, parent=None):
         )
     is_integer_type = np.issubdtype(layer.dtype, np.integer)
 
+    d_range = getattr(layer, range_attr)
     popup = QRangeSliderPopup(
         initial_values=getattr(layer, attr),
-        data_range=getattr(layer, range_attr),
+        data_range=d_range,
         collapsible=False,
-        precision=(0 if is_integer_type else 2),
+        precision=(
+            0
+            if is_integer_type
+            # scale precision with the log of the data range order of magnitude
+            # eg.   0 - 1   (0 order of mag)  -> 3 decimal places
+            #       0 - 10  (1 order of mag)  -> 2 decimals
+            #       0 - 100 (2 orders of mag) -> 1 decimal
+            #       ≥ 3 orders of mag -> no decimals
+            else int(max(3 - np.log10(max(d_range[1] - d_range[0], 0.01)), 0))
+        ),
         parent=parent,
     )
 
diff --git a/napari/_qt/layers/tests/test_qt_image_base_layer_.py b/napari/_qt/layers/tests/test_qt_image_base_layer_.py
index c84c70ee74c..50959f02768 100644
--- a/napari/_qt/layers/tests/test_qt_image_base_layer_.py
+++ b/napari/_qt/layers/tests/test_qt_image_base_layer_.py
@@ -6,7 +6,10 @@
 from qtpy.QtCore import Qt
 from qtpy.QtWidgets import QPushButton
 
-from napari._qt.layers.qt_image_base_layer import QtBaseImageControls
+from napari._qt.layers.qt_image_base_layer import (
+    QtBaseImageControls,
+    create_range_popup,
+)
 from napari.layers import Image, Surface
 
 _IMAGE = np.arange(100).astype(np.uint16).reshape((10, 10))
@@ -72,3 +75,22 @@ def test_range_popup_clim_buttons(qtbot, layer):
         assert tuple(qtctrl.contrastLimitsSlider.range()) == (0, 2 ** 16 - 1)
     else:
         assert rangebtn is None
+
+
+@pytest.mark.parametrize('mag', [-12, -9, -3, 0, 2, 4, 6])
+def test_clim_slider_step_size_and_precision(qtbot, mag):
+    """Make sure the slider has a reasonable step size and precision.
+
+    ...across a broad range of orders of magnitude.
+    """
+    layer = Image(np.random.rand(20, 20) / 10 ** mag)
+    popup = create_range_popup(layer, 'contrast_limits')
+
+    # the range slider popup labels should have a number of decimal points that
+    # is inversely proportional to the order of magnitude of the range of data,
+    # but should never be greater than 5 or less than 0
+    assert popup.precision == max(min(mag + 3, 5), 0)
+
+    # the slider step size should also be inversely proportional to the data
+    # range, with 1000 steps across the data range
+    assert np.ceil(popup.slider._step * 10 ** (mag + 4)) == 10
diff --git a/napari/_qt/qt_range_slider.py b/napari/_qt/qt_range_slider.py
index 56df381c51c..27facc007b6 100644
--- a/napari/_qt/qt_range_slider.py
+++ b/napari/_qt/qt_range_slider.py
@@ -77,7 +77,13 @@ def __init__(
 
         self.setRange((0, 100) if data_range is None else data_range)
         self.setValues((20, 80) if initial_values is None else initial_values)
-        self.setStep(0.01 if step_size is None else step_size)
+        if step_size is None:
+            # pick an appropriate slider step size based on the data range
+            if data_range is not None:
+                step_size = (data_range[1] - data_range[0]) / 1000
+            else:
+                step_size = 0.001
+        self.setStep(step_size)
         if not parent:
             if 'HRange' in self.__class__.__name__:
                 self.setGeometry(200, 200, 200, 20)