diff --git a/docs/Fixed-or-Improved-Logics.md b/docs/Fixed-or-Improved-Logics.md
index b999d606e2..de71110ad6 100644
--- a/docs/Fixed-or-Improved-Logics.md
+++ b/docs/Fixed-or-Improved-Logics.md
@@ -2111,7 +2111,7 @@ Conventional.IgnoreUnits=false  ; boolean
 
 ### Customizable Warhead trigger conditions
 
-- It is now possible to make warheads only trigger when target's (TechnoTypes only) HP is above/below or equal to certain percentage. Both conditions need to evaluate to true in order for the warhead to trigger.
+- `AffectsBelowPercent` and `AffectsAbovePercent` can be used to set the health percentage thresholds that target needs to be below/equal and/or above of for the Warhead to detonate. If target has zero health left this check is bypassed.
 - If set to `false`, `AffectsNeutral` makes the warhead can't damage or affect target that belongs to neutral house.
 - If set to `false`, `EffectsRequireVerses` makes the Phobos-introduced warhead effects trigger even if it can't damage the target because of it's current ArmorType (e.g. 0% in `Verses`).
 
diff --git a/docs/New-or-Enhanced-Logics.md b/docs/New-or-Enhanced-Logics.md
index 52818ffeaa..b3ada3a755 100644
--- a/docs/New-or-Enhanced-Logics.md
+++ b/docs/New-or-Enhanced-Logics.md
@@ -2119,7 +2119,7 @@ RemoveMindControl=false  ; boolean
   - `Crit.Warhead.FullDetonation` controls whether or not the Warhead is detonated fully on the targets (as part of a dummy weapon) or simply deals area damage and applies Phobos' Warhead effects.
   - `Crit.Affects` can be used to customize types of targets that this Warhead can deal critical hits against. Critical hits cannot affect empty cells or cells containing only TerrainTypes, overlays etc.
   - `Crit.AffectsHouses` can be used to customize houses that this Warhead can deal critical hits against.
-  - `Crit.AffectBelowPercent` and `Crit.AffectsAbovePercent` can be used to set the health percentage that targets must be below or above respectively to be affected by critical hits.
+  - `Crit.AffectBelowPercent` and `Crit.AffectsAbovePercent` can be used to set the health percentage that targets must be above and/or below/equal to respectively to be affected by critical hits. If target has zero health left this check is bypassed.
   - `Crit.AnimList` can be used to set a list of animations used instead of Warhead's `AnimList` if Warhead deals a critical hit to even one target. If `Crit.AnimList.PickRandom` is set (defaults to `AnimList.PickRandom`) then the animation is chosen randomly from the list. If `Crit.AnimList.CreateAll` is set (defaults to `AnimList.CreateAll`), all animations from the list are created.
     - `Crit.AnimOnAffectedTargets`, if set, makes the animation(s) from `Crit.AnimList` play on each affected target *in addition* to animation from Warhead's `AnimList` playing as normal instead of replacing `AnimList` animation. Note that because these animations are independent from `AnimList`, `Crit.AnimList.PickRandom` and `Crit.AnimList.CreateAll` will not default to their `AnimList` counterparts here and need to be explicitly set if needed.
   - `Crit.ActiveChanceAnims` can be used to set animation to be always displayed at the Warhead's detonation coordinates if the current Warhead has a chance to critically hit. If more than one animation is listed, a random one is selected.
@@ -2657,7 +2657,7 @@ This function is only used as an additional scattering visual display, which is
 *`Weapon target filter - different weapon used against enemies & allies as well as units & buildings in [Project Phantom](https://www.moddb.com/mods/project-phantom)*
 
 - You can now specify which targets or houses a weapon can fire at. This also affects weapon selection, other than certain special cases where the selection is fixed.
-  - `CanTarget.MaxHealth` and `CanTarget.MinHealth` set health percentage thresholds for allowed targets (TechnoTypes only), maximum/minimum respectively.
+  - `CanTarget.MaxHealth` and `CanTarget.MinHealth` set health percentage thresholds for allowed targets (TechnoTypes only) that the target's health must be above and/or below/equal to, respectively. If target has zero health left this check is bypassed.
 
 In `rulesmd.ini`:
 ```ini
diff --git a/src/Ext/Techno/Body.cpp b/src/Ext/Techno/Body.cpp
index a7dfb25842..5da5a46ba4 100644
--- a/src/Ext/Techno/Body.cpp
+++ b/src/Ext/Techno/Body.cpp
@@ -727,8 +727,11 @@ bool TechnoExt::HandleDelayedFireWithPauseSequence(TechnoClass* pThis, int weapo
 
 bool TechnoExt::IsHealthInThreshold(TechnoClass* pObject, double min, double max)
 {
+	if (!pObject->Health && !pObject->GetType()->Strength)
+		return true;
+
 	const double hp = pObject->GetHealthPercentage();
-	return hp <= max && hp >= min;
+	return (hp > 0 ? hp > min : hp >= min) && hp <= max;
 }
 
 bool TechnoExt::CannotMove(UnitClass* pThis)