diff --git a/src/modules/sbstudio/plugin/model/safety_check.py b/src/modules/sbstudio/plugin/model/safety_check.py
index 62f549f..59e93da 100644
--- a/src/modules/sbstudio/plugin/model/safety_check.py
+++ b/src/modules/sbstudio/plugin/model/safety_check.py
@@ -266,6 +266,14 @@ def min_distance_is_valid(self) -> bool:
         # on macOS, hence we need to exclude large min distances
         return self.min_distance > 0 and self.min_distance < 100000
 
+    @property
+    def min_navigation_altitude_is_valid(self) -> bool:
+        """Retuns whether the minimum navigation altitude property can be
+        considered valid. Right now we use zero to denote cases when there are
+        no drones in the scene at all.
+        """
+        return self.min_navigation_altitude > 0
+
     @property
     def max_altitude_is_valid(self) -> bool:
         """Retuns whether the maximum altitude property can be considered valid.
@@ -294,7 +302,11 @@ def should_show_altitude_warning(self) -> bool:
         return (
             self.altitude_warning_enabled
             and self.max_altitude_is_valid
-            and self.max_altitude > self.altitude_warning_threshold
+            and self.min_navigation_altitude_is_valid
+            and (
+                self.max_altitude > self.altitude_warning_threshold
+                or self.min_altitude < self.min_navigation_altitude
+            )
         )
 
     @property
diff --git a/src/modules/sbstudio/plugin/tasks/safety_check.py b/src/modules/sbstudio/plugin/tasks/safety_check.py
index d43e3b2..a68a635 100644
--- a/src/modules/sbstudio/plugin/tasks/safety_check.py
+++ b/src/modules/sbstudio/plugin/tasks/safety_check.py
@@ -3,13 +3,16 @@
 frame.
 """
 
+from __future__ import annotations
+
 import bpy
 
 from contextlib import contextmanager
 from math import hypot
-from typing import Iterator
+from typing import Iterator, TYPE_CHECKING
 
 from sbstudio.math.nearest_neighbors import find_nearest_neighbors
+from sbstudio.model.types import Coordinate3D
 from sbstudio.plugin.utils.evaluator import get_position_of_object
 from sbstudio.plugin.constants import Collections
 from sbstudio.utils import LRUCache
@@ -18,13 +21,20 @@
 
 from .base import Task
 
+if TYPE_CHECKING:
+    from bpy.types import Scene
+
 
 # TODO(ntamas): make the nearest-neighbor calculation debounced when we have
 # lots of drones, but currently we are good with, say 100 drones
 
+PositionSnapshot = dict[str, Coordinate3D]
+VelocitySnapshot = dict[str, Coordinate3D]
+
+
 #: Cache that stores the positions in the last few frames visited by the user
 #: in the hope that we can estimate the velocities from it in the current frame
-_position_snapshot_cache = LRUCache(5)
+_position_snapshot_cache: LRUCache[int, PositionSnapshot] = LRUCache(5)
 
 #: Suspension counter. Safety checks are suspended if this counter is positive
 _suspension_counter = 0
@@ -34,14 +44,18 @@
 _ZERO = (0.0, 0.0, 0.0)
 
 
-def create_position_snapshot_for_drones_in_collection(collection, *, frame):
+def create_position_snapshot_for_drones_in_collection(
+    collection, *, frame: int
+) -> PositionSnapshot:
     """Create a dictionary mapping the names of the drones in the given
     collection to their positions.
     """
     return {drone.name: get_position_of_object(drone) for drone in collection.objects}
 
 
-def estimate_velocities_of_drones_at_frame(snapshot, *, frame, scene):
+def estimate_velocities_of_drones_at_frame(
+    snapshot: PositionSnapshot, *, frame: int, scene: Scene
+) -> VelocitySnapshot:
     """Attempts to estimate the velocities of the drones in the given frame,
     using the given snapshot for the frame and the current data in the
     position snapshot cache.
@@ -94,7 +108,7 @@ def estimate_velocities_of_drones_at_frame(snapshot, *, frame, scene):
 
 
 # @debounced(delay=0.1)
-def run_safety_check(scene, depsgraph):
+def run_safety_check(scene: Scene, depsgraph) -> None:
     global _suspension_counter
     if _suspension_counter > 0:
         return
@@ -110,11 +124,15 @@ def run_safety_check(scene, depsgraph):
         safety_check.clear_safety_check_result()
         return
 
-    # Get the thresholds from the safety check object
+    # Get the altitude thresholds from the safety check object
     if safety_check.altitude_warning_threshold:
+        min_altitude = safety_check.min_navigation_altitude
         max_altitude = safety_check.altitude_warning_threshold
     else:
+        min_altitude = None
         max_altitude = None
+
+    # Get the velocity thresholds from the safety check object
     if safety_check.velocity_warning_enabled:
         max_velocity_xy = safety_check.velocity_xy_warning_threshold
         max_velocity_z_down = safety_check.effective_velocity_z_threshold_down
@@ -130,14 +148,16 @@ def run_safety_check(scene, depsgraph):
     storyboard = scene.skybrush.storyboard
     formation_status = storyboard.get_formation_status_at_frame(frame)
 
-    # Check min/max altitude
+    # Prepare position snapshot
     positions = list(snapshot.values())
-    if max_altitude is not None:
-        drones_over_max_altitude = [
-            position for position in positions if position[2] >= max_altitude
-        ]
-    else:
-        drones_over_max_altitude = []
+
+    # Prepare velocity snapshot
+    velocity_snapshot = estimate_velocities_of_drones_at_frame(
+        snapshot, frame=frame, scene=scene
+    )
+    velocities = list(velocity_snapshot.values())
+
+    # Find min/max altitude for reporting purposes
     max_altitude_found = (
         max(position[2] for position in positions) if positions else 0.0
     )
@@ -145,38 +165,55 @@ def run_safety_check(scene, depsgraph):
         min(position[2] for position in positions) if positions else 0.0
     )
 
+    # Check max altitude constraint
+    if max_altitude is not None:
+        drones_over_max_altitude = [
+            position for position in positions if position[2] >= max_altitude
+        ]
+    else:
+        drones_over_max_altitude = []
+
     # Check nearest neighbors
     nearest_neighbors = find_nearest_neighbors(positions)
 
-    # Check velocities
-    max_velocity_xy_found = None
-    velocity_snapshot = estimate_velocities_of_drones_at_frame(
-        snapshot, frame=frame, scene=scene
-    )
-    velocities = list(velocity_snapshot.values())
-
+    # Check velocities in XY direction
     max_velocity_xy_found = (
         max(hypot(vel[0], vel[1]) for vel in velocities) if velocities else 0.0
     )
-    if max_velocity_xy is not None:
-        drones_over_max_velocity_xy = [
+    drones_over_max_velocity_xy = (
+        [
             snapshot.get(name, _ZERO)
             for name, vel in velocity_snapshot.items()
             if hypot(vel[0], vel[1]) > max_velocity_xy
         ]
-    else:
-        drones_over_max_velocity_xy = []
+        if max_velocity_xy is not None
+        else []
+    )
 
+    # Check velocities in Z direction
     upper = max(0.0, max(vel[2] for vel in velocities)) if velocities else 0.0
     lower = min(0.0, min(vel[2] for vel in velocities)) if velocities else 0.0
-    if max_velocity_z_up is not None and max_velocity_z_down is not None:
-        drones_over_max_velocity_z = [
+    drones_over_max_velocity_z = (
+        [
             snapshot.get(name, _ZERO)
             for name, vel in velocity_snapshot.items()
             if vel[2] > max_velocity_z_up or vel[2] < -max_velocity_z_down
         ]
-    else:
-        drones_over_max_velocity_z = []
+        if max_velocity_z_up is not None and max_velocity_z_down is not None
+        else []
+    )
+
+    # Find drones moving horizontally below min navigation altitude
+    drones_below_min_nav_altitude = (
+        [
+            pos
+            for name, vel in velocity_snapshot.items()
+            if (vel[0] != 0 or vel[1] != 0)
+            and (pos := snapshot.get(name, _ZERO))[2] < min_altitude
+        ]
+        if min_altitude is not None and min_altitude_found < min_altitude
+        else []
+    )
 
     safety_check.set_safety_check_result(
         formation_status=formation_status,
@@ -189,6 +226,7 @@ def run_safety_check(scene, depsgraph):
         max_velocity_z_up=upper,
         max_velocity_z_down=abs(lower),
         drones_over_max_velocity_z=drones_over_max_velocity_z,
+        drones_below_min_nav_altitude=drones_below_min_nav_altitude,
     )