diff --git a/src/newgrf.cpp b/src/newgrf.cpp
index e25334f662..a4c7aa1fbb 100644
--- a/src/newgrf.cpp
+++ b/src/newgrf.cpp
@@ -6915,7 +6915,13 @@ static void OptimiseVarAction2Adjust(VarAction2OptimiseState &state, const GrfSp
 					}
 					if (adjust.and_mask <= 1) state.inference = prev_inference & (VA2AIF_SIGNED_NON_NEGATIVE | VA2AIF_ONE_OR_ZERO);
 					state.inference |= prev_inference & (VA2AIF_SIGNED_NON_NEGATIVE | VA2AIF_ONE_OR_ZERO) & non_const_var_inference;
-					if ((non_const_var_inference & VA2AIF_ONE_OR_ZERO) || (adjust.and_mask <= 1)) adjust.adjust_flags |= DSGAF_SKIP_ON_LSB_SET;
+					if ((non_const_var_inference & VA2AIF_ONE_OR_ZERO) || (adjust.and_mask <= 1)) {
+						adjust.adjust_flags |= DSGAF_SKIP_ON_LSB_SET;
+						if (prev_inference & VA2AIF_ONE_OR_ZERO) {
+							adjust.adjust_flags |= DSGAF_JUMP_INS_HINT;
+							group->dsg_flags |= DSGF_CHECK_INSERT_JUMP;
+						}
+					}
 					try_merge_with_previous();
 					break;
 				case DSGA_OP_XOR:
@@ -7332,7 +7338,7 @@ static bool OptimiseVarAction2DeterministicSpriteGroupExpensiveVarsInner(Determi
 		bool seen_first = false;
 		for (int j = end; j >= start; j--) {
 			DeterministicSpriteGroupAdjust &adjust = group->adjusts[j];
-			if (seen_first && adjust.operation == DSGA_OP_JZ && condition_depth > 0) {
+			if (seen_first && IsEvalAdjustJumpOperation(adjust.operation) && condition_depth > 0) {
 				/* Do not insert the STO_NC inside a conditional block when it is also needed outside the block */
 				condition_depth--;
 				insert_pos = j;
@@ -7645,7 +7651,7 @@ static void OptimiseVarAction2DeterministicSpriteGroupInsertJumps(DeterministicS
 				if (prev.operation == DSGA_OP_STO && (prev.type != DSGA_TYPE_NONE || prev.variable != 0x1A || prev.shift_num != 0 || prev.and_mask >= 0x100)) break;
 				if (prev.operation == DSGA_OP_STO_NC && prev.divmod_val >= 0x100) break;
 				if (prev.operation == DSGA_OP_STOP) break;
-				if (prev.operation == DSGA_OP_JZ) break;
+				if (IsEvalAdjustJumpOperation(prev.operation)) break;
 				if (prev.variable == 0x7E) break;
 
 				/* Reached a store which can't be skipped over because the value is needed later */
@@ -7676,8 +7682,8 @@ static void OptimiseVarAction2DeterministicSpriteGroupInsertJumps(DeterministicS
 					current.adjust_flags &= ~DSGAF_END_BLOCK;
 					current.jump = 0;
 				}
-				current.operation = DSGA_OP_JZ;
-				current.adjust_flags &= ~(DSGAF_JUMP_INS_HINT | DSGAF_SKIP_ON_ZERO);
+				current.operation = (current.adjust_flags & DSGAF_SKIP_ON_LSB_SET) ? DSGA_OP_JNZ : DSGA_OP_JZ;
+				current.adjust_flags &= ~(DSGAF_JUMP_INS_HINT | DSGAF_SKIP_ON_ZERO | DSGAF_SKIP_ON_LSB_SET);
 				mark_end_block(group->adjusts[i - 1], 1);
 				group->adjusts.erase(group->adjusts.begin() + i);
 				if (j >= 0 && current.variable == 0x7D && (current.adjust_flags & DSGAF_LAST_VAR_READ)) {
@@ -7706,7 +7712,7 @@ struct ResolveJumpInnerResult {
 static ResolveJumpInnerResult OptimiseVarAction2DeterministicSpriteResolveJumpsInner(DeterministicSpriteGroup *group, const uint start)
 {
 	for (uint i = start + 1; i < (uint)group->adjusts.size(); i++) {
-		if (group->adjusts[i].operation == DSGA_OP_JZ) {
+		if (IsEvalAdjustJumpOperation(group->adjusts[i].operation)) {
 			ResolveJumpInnerResult result = OptimiseVarAction2DeterministicSpriteResolveJumpsInner(group, i);
 			i = result.end_index;
 			if (result.end_block_remaining > 0) {
@@ -7727,7 +7733,7 @@ static void OptimiseVarAction2DeterministicSpriteResolveJumps(DeterministicSprit
 	if (HasGrfOptimiserFlag(NGOF_NO_OPT_VARACT2_INSERT_JUMPS)) return;
 
 	for (uint i = 0; i < (uint)group->adjusts.size(); i++) {
-		if (group->adjusts[i].operation == DSGA_OP_JZ) {
+		if (IsEvalAdjustJumpOperation(group->adjusts[i].operation)) {
 			ResolveJumpInnerResult result = OptimiseVarAction2DeterministicSpriteResolveJumpsInner(group, i);
 			i = result.end_index;
 			assert(result.end_block_remaining == 0);
diff --git a/src/newgrf_spritegroup.cpp b/src/newgrf_spritegroup.cpp
index 9040cd3531..97f16c41e4 100644
--- a/src/newgrf_spritegroup.cpp
+++ b/src/newgrf_spritegroup.cpp
@@ -212,6 +212,16 @@ static U EvalAdjustT(const DeterministicSpriteGroupAdjust &adjust, ScopeResolver
 				return last_value;
 			}
 		}
+		case DSGA_OP_JNZ: {
+			if (value != 0 && adjust_iter != nullptr) {
+				/* Jump */
+				(*adjust_iter) += adjust.jump;
+				return value;
+			} else {
+				/* Don't jump */
+				return last_value;
+			}
+		}
 		default:           return value;
 	}
 }
@@ -700,6 +710,7 @@ static const char *_dsg_op_special_names[] {
 	"STO_NC",
 	"ABS",
 	"JZ",
+	"JNZ",
 };
 static_assert(lengthof(_dsg_op_special_names) == DSGA_OP_SPECIAL_END - DSGA_OP_TERNARY);
 
@@ -753,7 +764,7 @@ static char *DumpSpriteGroupAdjust(char *p, const char *last, const Deterministi
 		}
 	};
 
-	if (adjust.operation == DSGA_OP_JZ) {
+	if (IsEvalAdjustJumpOperation(adjust.operation)) {
 		conditional_indent++;
 	}
 	if (adjust.adjust_flags & DSGAF_END_BLOCK) {
@@ -801,7 +812,7 @@ static char *DumpSpriteGroupAdjust(char *p, const char *last, const Deterministi
 	}
 	p += seprintf(p, last, ", op: ");
 	p = GetAdjustOperationName(p, last, adjust.operation);
-	if (adjust.operation == DSGA_OP_JZ) {
+	if (IsEvalAdjustJumpOperation(adjust.operation)) {
 		p += seprintf(p, last, " +%u", adjust.jump);
 	}
 	append_flags();
diff --git a/src/newgrf_spritegroup.h b/src/newgrf_spritegroup.h
index 42990806a6..920c1a5dfd 100644
--- a/src/newgrf_spritegroup.h
+++ b/src/newgrf_spritegroup.h
@@ -207,6 +207,7 @@ enum DeterministicSpriteGroupAdjustOperation : uint8 {
 	DSGA_OP_STO_NC,         ///< store b into temporary storage, indexed by c. return a
 	DSGA_OP_ABS,            ///< abs(a)
 	DSGA_OP_JZ,             ///< jump forward fixed number of adjusts (to adjust after DSGAF_END_BLOCK marker (taking into account nesting)) if b is zero. return 0 if jumped, return a if not jumped
+	DSGA_OP_JNZ,            ///< jump forward fixed number of adjusts (to adjust after DSGAF_END_BLOCK marker (taking into account nesting)) if b is non-zero. return b if jumped, return a if not jumped
 
 	DSGA_OP_SPECIAL_END,
 };
@@ -402,6 +403,18 @@ inline bool IsEvalAdjustWithZeroLastValueAlwaysZero(DeterministicSpriteGroupAdju
 	}
 }
 
+inline bool IsEvalAdjustJumpOperation(DeterministicSpriteGroupAdjustOperation op)
+{
+	switch (op) {
+		case DSGA_OP_JZ:
+		case DSGA_OP_JNZ:
+			return true;
+
+		default:
+			return false;
+	}
+}
+
 inline bool IsConstantComparisonAdjustType(DeterministicSpriteGroupAdjustType adjust_type)
 {
 	switch (adjust_type) {