diff --git a/src/mono/mono/mini/interp/interp.c b/src/mono/mono/mini/interp/interp.c
index 6db2f621167d95..0e262c06d71eaa 100644
--- a/src/mono/mono/mini/interp/interp.c
+++ b/src/mono/mono/mini/interp/interp.c
@@ -5472,33 +5472,29 @@ MINT_IN_CASE(MINT_BRTRUE_I8_SP) ZEROP_SP(gint64, !=); MINT_IN_BREAK;
 		}
 		MINT_IN_CASE(MINT_CONV_OVF_U8_R4) {
 			float val = LOCAL_VAR (ip [2], float);
-			if (mono_isnan (val) || mono_trunc (val) != (guint64)val)
+			if (!mono_try_trunc_u64 (val, (guint64*)(locals + ip [1])))
 				THROW_EX (mono_get_exception_overflow (), ip);
-			LOCAL_VAR (ip [1], guint64) = (guint64)val;
 			ip += 3;
 			MINT_IN_BREAK;
 		}
 		MINT_IN_CASE(MINT_CONV_OVF_U8_R8) {
 			double val = LOCAL_VAR (ip [2], double);
-			if (mono_isnan (val) || mono_trunc (val) != (guint64)val)
+			if (!mono_try_trunc_u64 (val, (guint64*)(locals + ip [1])))
 				THROW_EX (mono_get_exception_overflow (), ip);
-			LOCAL_VAR (ip [1], guint64) = (guint64)val;
 			ip += 3;
 			MINT_IN_BREAK;
 		}
 		MINT_IN_CASE(MINT_CONV_OVF_I8_R4) {
 			float val = LOCAL_VAR (ip [2], float);
-			if (mono_isnan (val) || mono_trunc (val) != (gint64)val)
+			if (!mono_try_trunc_i64 (val, (gint64*)(locals + ip [1])))
 				THROW_EX (mono_get_exception_overflow (), ip);
-			LOCAL_VAR (ip [1], gint64) = (gint64)val;
 			ip += 3;
 			MINT_IN_BREAK;
 		}
 		MINT_IN_CASE(MINT_CONV_OVF_I8_R8) {
 			double val = LOCAL_VAR (ip [2], double);
-			if (mono_isnan (val) || mono_trunc (val) != (gint64)val)
+			if (!mono_try_trunc_i64 (val, (gint64*)(locals + ip [1])))
 				THROW_EX (mono_get_exception_overflow (), ip);
-			LOCAL_VAR (ip [1], gint64) = (gint64)val;
 			ip += 3;
 			MINT_IN_BREAK;
 		}
@@ -5800,17 +5796,20 @@ MINT_IN_CASE(MINT_BRTRUE_I8_SP) ZEROP_SP(gint64, !=); MINT_IN_BREAK;
 		}
 		MINT_IN_CASE(MINT_CONV_OVF_I4_R4) {
 			float val = LOCAL_VAR (ip [2], float);
-			if (mono_isnan (val) || mono_trunc (val) != (gint32)val)
+			double val_r8 = (double)val;
+			if (val_r8 > ((double)G_MININT32 - 1) && val_r8 < ((double)G_MAXINT32 + 1))
+				LOCAL_VAR (ip [1], gint32) = (gint32) val;
+			else
 				THROW_EX (mono_get_exception_overflow (), ip);
-			LOCAL_VAR (ip [1], gint32) = (gint32) val;
 			ip += 3;
 			MINT_IN_BREAK;
 		}
 		MINT_IN_CASE(MINT_CONV_OVF_I4_R8) {
 			double val = LOCAL_VAR (ip [2], double);
-			if (val < G_MININT32 || val > G_MAXINT32 || isnan (val))
+			if (val > ((double)G_MININT32 - 1) && val < ((double)G_MAXINT32 + 1))
+				LOCAL_VAR (ip [1], gint32) = (gint32) val;
+			else
 				THROW_EX (mono_get_exception_overflow (), ip);
-			LOCAL_VAR (ip [1], gint32) = (gint32)val;
 			ip += 3;
 			MINT_IN_BREAK;
 		}
@@ -5832,17 +5831,20 @@ MINT_IN_CASE(MINT_BRTRUE_I8_SP) ZEROP_SP(gint64, !=); MINT_IN_BREAK;
 		}
 		MINT_IN_CASE(MINT_CONV_OVF_U4_R4) {
 			float val = LOCAL_VAR (ip [2], float);
-			if (mono_isnan (val) || mono_trunc (val) != (guint32)val)
+			double val_r8 = val;
+			if (val_r8 > -1.0 && val_r8 < ((double)G_MAXUINT32 + 1))
+				LOCAL_VAR (ip [1], gint32) = (guint32)val;
+			else
 				THROW_EX (mono_get_exception_overflow (), ip);
-			LOCAL_VAR (ip [1], gint32) = (guint32)val;
 			ip += 3;
 			MINT_IN_BREAK;
 		}
 		MINT_IN_CASE(MINT_CONV_OVF_U4_R8) {
 			double val = LOCAL_VAR (ip [2], double);
-			if (val < 0 || val > G_MAXUINT32 || isnan (val))
+			if (val > -1.0 && val < ((double)G_MAXUINT32 + 1))
+				LOCAL_VAR (ip [1], gint32) = (guint32)val;
+			else
 				THROW_EX (mono_get_exception_overflow (), ip);
-			LOCAL_VAR (ip [1], gint32) = (guint32) val;
 			ip += 3;
 			MINT_IN_BREAK;
 		}
@@ -5880,17 +5882,19 @@ MINT_IN_CASE(MINT_BRTRUE_I8_SP) ZEROP_SP(gint64, !=); MINT_IN_BREAK;
 		}
 		MINT_IN_CASE(MINT_CONV_OVF_I2_R4) {
 			float val = LOCAL_VAR (ip [2], float);
-			if (val < G_MININT16 || val > G_MAXINT16 || isnan (val))
+			if (val > (G_MININT16 - 1) && val < (G_MAXINT16 + 1))
+				LOCAL_VAR (ip [1], gint32) = (gint16) val;
+			else
 				THROW_EX (mono_get_exception_overflow (), ip);
-			LOCAL_VAR (ip [1], gint32) = (gint16) val;
 			ip += 3;
 			MINT_IN_BREAK;
 		}
 		MINT_IN_CASE(MINT_CONV_OVF_I2_R8) {
 			double val = LOCAL_VAR (ip [2], double);
-			if (val < G_MININT16 || val > G_MAXINT16 || isnan (val))
+			if (val > (G_MININT16 - 1) && val < (G_MAXINT16 + 1))
+				LOCAL_VAR (ip [1], gint32) = (gint16) val;
+			else
 				THROW_EX (mono_get_exception_overflow (), ip);
-			LOCAL_VAR (ip [1], gint32) = (gint16) val;
 			ip += 3;
 			MINT_IN_BREAK;
 		}
@@ -5912,17 +5916,19 @@ MINT_IN_CASE(MINT_BRTRUE_I8_SP) ZEROP_SP(gint64, !=); MINT_IN_BREAK;
 		}
 		MINT_IN_CASE(MINT_CONV_OVF_U2_R4) {
 			float val = LOCAL_VAR (ip [2], float);
-			if (val < 0 || val > G_MAXUINT16 || isnan (val))
+			if (val > -1.0f && val < (G_MAXUINT16 + 1))
+				LOCAL_VAR (ip [1], gint32) = (guint16) val;
+			else
 				THROW_EX (mono_get_exception_overflow (), ip);
-			LOCAL_VAR (ip [1], gint32) = (guint16) val;
 			ip += 3;
 			MINT_IN_BREAK;
 		}
 		MINT_IN_CASE(MINT_CONV_OVF_U2_R8) {
 			double val = LOCAL_VAR (ip [2], double);
-			if (val < 0 || val > G_MAXUINT16 || isnan (val))
+			if (val > -1.0 && val < (G_MAXUINT16 + 1))
+				LOCAL_VAR (ip [1], gint32) = (guint16) val;
+			else
 				THROW_EX (mono_get_exception_overflow (), ip);
-			LOCAL_VAR (ip [1], gint32) = (guint16) val;
 			ip += 3;
 			MINT_IN_BREAK;
 		}
@@ -5960,17 +5966,19 @@ MINT_IN_CASE(MINT_BRTRUE_I8_SP) ZEROP_SP(gint64, !=); MINT_IN_BREAK;
 		}
 		MINT_IN_CASE(MINT_CONV_OVF_I1_R4) {
 			float val = LOCAL_VAR (ip [2], float);
-			if (val < G_MININT8 || val > G_MAXINT8 || isnan (val))
+			if (val > (G_MININT8 - 1) && val < (G_MAXINT8 + 1))
+				LOCAL_VAR (ip [1], gint32) = (gint8) val;
+			else
 				THROW_EX (mono_get_exception_overflow (), ip);
-			LOCAL_VAR (ip [1], gint32) = (gint8) val;
 			ip += 3;
 			MINT_IN_BREAK;
 		}
 		MINT_IN_CASE(MINT_CONV_OVF_I1_R8) {
 			double val = LOCAL_VAR (ip [2], double);
-			if (val < G_MININT8 || val > G_MAXINT8 || isnan (val))
+			if (val > (G_MININT8 - 1) && val < (G_MAXINT8 + 1))
+				LOCAL_VAR (ip [1], gint32) = (gint8) val;
+			else
 				THROW_EX (mono_get_exception_overflow (), ip);
-			LOCAL_VAR (ip [1], gint32) = (gint8) val;
 			ip += 3;
 			MINT_IN_BREAK;
 		}
@@ -5992,17 +6000,19 @@ MINT_IN_CASE(MINT_BRTRUE_I8_SP) ZEROP_SP(gint64, !=); MINT_IN_BREAK;
 		}
 		MINT_IN_CASE(MINT_CONV_OVF_U1_R4) {
 			float val = LOCAL_VAR (ip [2], float);
-			if (val < 0 || val > G_MAXUINT8 || isnan (val))
+			if (val > -1.0f && val < (G_MAXUINT8 + 1))
+				LOCAL_VAR (ip [1], gint32) = (guint8)val;
+			else
 				THROW_EX (mono_get_exception_overflow (), ip);
-			LOCAL_VAR (ip [1], gint32) = (guint8) val;
 			ip += 3;
 			MINT_IN_BREAK;
 		}
 		MINT_IN_CASE(MINT_CONV_OVF_U1_R8) {
 			double val = LOCAL_VAR (ip [2], double);
-			if (val < 0 || val > G_MAXUINT8 || isnan (val))
+			if (val > -1.0 && val < (G_MAXUINT8 + 1))
+				LOCAL_VAR (ip [1], gint32) = (guint8)val;
+			else
 				THROW_EX (mono_get_exception_overflow (), ip);
-			LOCAL_VAR (ip [1], gint32) = (guint8) val;
 			ip += 3;
 			MINT_IN_BREAK;
 		}
diff --git a/src/mono/mono/mini/local-propagation.c b/src/mono/mono/mini/local-propagation.c
index 3bd878e66b56a0..19801edd1f2814 100644
--- a/src/mono/mono/mini/local-propagation.c
+++ b/src/mono/mono/mini/local-propagation.c
@@ -223,7 +223,7 @@ mono_strength_reduction_division (MonoCompile *cfg, MonoInst *ins)
 			guint32 tmp_regi;
 #endif
 			struct magic_signed mag;
-			int power2 = mono_is_power_of_two (ins->inst_imm);
+			int power2 = (ins->inst_imm > 0) ? mono_is_power_of_two (ins->inst_imm) : -1;
 			/* The decomposition doesn't handle exception throwing */
 			/* Optimization with MUL does not apply for -1, 0 and 1 divisors */
 			if (ins->inst_imm == 0 || ins->inst_imm == -1) {
@@ -350,7 +350,7 @@ mono_strength_reduction_ins (MonoCompile *cfg, MonoInst *ins, const char **spec)
 			ins->opcode = OP_INEG;
 		} else if ((ins->opcode == OP_LMUL_IMM) && (ins->inst_imm == -1)) {
 			ins->opcode = OP_LNEG;
-		} else {
+		} else if (ins->inst_imm > 0) {
 			int power2 = mono_is_power_of_two (ins->inst_imm);
 			if (power2 >= 0) {
 				ins->opcode = (ins->opcode == OP_MUL_IMM) ? OP_SHL_IMM : ((ins->opcode == OP_LMUL_IMM) ? OP_LSHL_IMM : OP_ISHL_IMM);
diff --git a/src/mono/mono/mini/mini-arm.c b/src/mono/mono/mini/mini-arm.c
index 58c0cef04842e9..f22ba5b5a4a3b7 100644
--- a/src/mono/mono/mini/mini-arm.c
+++ b/src/mono/mono/mini/mini-arm.c
@@ -3466,7 +3466,7 @@ mono_arch_lowering_pass (MonoCompile *cfg, MonoBasicBlock *bb)
 				ins->inst_c0 = 0;
 				break;
 			}
-			imm8 = mono_is_power_of_two (ins->inst_imm);
+			imm8 = (ins->inst_imm > 0) ? mono_is_power_of_two (ins->inst_imm) : -1;
 			if (imm8 > 0) {
 				ins->opcode = OP_SHL_IMM;
 				ins->inst_imm = imm8;
diff --git a/src/mono/mono/mini/mini-mips.c b/src/mono/mono/mini/mini-mips.c
index 9a353ce85fa1ea..b77252e7515715 100644
--- a/src/mono/mono/mini/mini-mips.c
+++ b/src/mono/mono/mini/mini-mips.c
@@ -1987,7 +1987,7 @@ mono_arch_peephole_pass_2 (MonoCompile *cfg, MonoBasicBlock *bb)
 					MONO_DELETE_INS (bb, ins);
 					continue;
 				}
-			} else {
+			} else if (ins->inst_imm > 0) {
 				int power2 = mono_is_power_of_two (ins->inst_imm);
 				if (power2 > 0) {
 					ins->opcode = OP_SHL_IMM;
@@ -2666,7 +2666,7 @@ mono_arch_lowering_pass (MonoCompile *cfg, MonoBasicBlock *bb)
 				ins->inst_c0 = 0;
 				break;
 			}
-			imm = mono_is_power_of_two (ins->inst_imm);
+			imm = (ins->inst_imm > 0) ? mono_is_power_of_two (ins->inst_imm) : -1;
 			if (imm > 0) {
 				ins->opcode = OP_SHL_IMM;
 				ins->inst_imm = imm;
diff --git a/src/mono/mono/mini/mini-ppc.c b/src/mono/mono/mini/mini-ppc.c
index 19097c9df89d91..e3de468cbac117 100644
--- a/src/mono/mono/mini/mini-ppc.c
+++ b/src/mono/mono/mini/mini-ppc.c
@@ -1963,7 +1963,7 @@ mono_arch_peephole_pass_2 (MonoCompile *cfg, MonoBasicBlock *bb)
 					MONO_DELETE_INS (bb, ins);
 					continue;
 				}
-			} else {
+			} else if (inst->inst_imm > 0) {
 				int power2 = mono_is_power_of_two (ins->inst_imm);
 				if (power2 > 0) {
 					ins->opcode = OP_SHL_IMM;
@@ -2537,7 +2537,7 @@ mono_arch_lowering_pass (MonoCompile *cfg, MonoBasicBlock *bb)
 				ins->inst_c0 = 0;
 				break;
 			}
-			imm = mono_is_power_of_two (ins->inst_imm);
+			imm = (ins->inst_imm > 0) ? mono_is_power_of_two (ins->inst_imm) : -1;
 			if (imm > 0) {
 				ins->opcode = OP_SHL_IMM;
 				ins->inst_imm = imm;
diff --git a/src/mono/mono/utils/mono-math.h b/src/mono/mono/utils/mono-math.h
index 0f535e8ca28629..a24a0a303a9efc 100644
--- a/src/mono/mono/utils/mono-math.h
+++ b/src/mono/mono/utils/mono-math.h
@@ -7,6 +7,7 @@
 
 #include <math.h>
 #include <mono/utils/mono-publib.h>
+#include <glib.h>
 
 // Instead of isfinite, isinf, isnan, etc.,
 // use mono_isfininite, mono_isinf, mono_isnan, etc.
@@ -99,4 +100,27 @@ mono_round_to_even (double x)
 	return copysign (floor_tmp, x);
 }
 
+static inline gboolean
+mono_try_trunc_i64 (double val, gint64 *out)
+{
+	const double two63  = 2147483648.0 * 4294967296.0;
+	// 0x402 is epsilon used to get us to the next value
+	if (val > (-two63 - 0x402) && val < two63) {
+		*out = (gint64)val;
+		return TRUE;
+	}
+	return FALSE;
+}
+
+static inline gboolean
+mono_try_trunc_u64 (double val, guint64 *out)
+{
+	const double two64  = 4294967296.0 * 4294967296.0;
+	if (val > -1.0 && val < two64) {
+		*out = (guint64)val;
+		return TRUE;
+	}
+	return FALSE;
+}
+
 #endif
diff --git a/src/tests/issues.targets b/src/tests/issues.targets
index 3712feb3d7731d..64cf26f78662eb 100644
--- a/src/tests/issues.targets
+++ b/src/tests/issues.targets
@@ -965,27 +965,9 @@
         </ExcludeList>
 
 
-        <ExcludeList Include="$(XunitTestBinBase)/JIT/Directed/Convert/value_numbering_checked_casts_of_constants/*">
-            <Issue>https://github.com/dotnet/runtime/issues/51323</Issue>
-        </ExcludeList>
-        <ExcludeList Include="$(XunitTestBinBase)/JIT/Methodical/int64/misc/longmul/*">
-            <Issue>https://github.com/dotnet/runtime/issues/51323</Issue>
-        </ExcludeList>
         <ExcludeList Include="$(XunitTestBinBase)/JIT/Directed/Convert/out_of_range_fp_to_int_conversions/*">
             <Issue>Mono does not define out of range fp to int conversions</Issue>
         </ExcludeList>
-        <ExcludeList Include="$(XunitTestBinBase)/JIT/Methodical/Overflow/FloatOvfToInt2_r/*">
-            <Issue>https://github.com/dotnet/runtime/issues/51323</Issue>
-        </ExcludeList>
-        <ExcludeList Include="$(XunitTestBinBase)/JIT/Methodical/Overflow/FloatOvfToInt2_ro/*">
-            <Issue>https://github.com/dotnet/runtime/issues/51323</Issue>
-        </ExcludeList>
-        <ExcludeList Include="$(XunitTestBinBase)/JIT/Methodical/Overflow/FloatOvfToInt2_d/*">
-            <Issue>https://github.com/dotnet/runtime/issues/51323</Issue>
-        </ExcludeList>
-        <ExcludeList Include="$(XunitTestBinBase)/JIT/Methodical/Overflow/FloatOvfToInt2_do/*">
-            <Issue>https://github.com/dotnet/runtime/issues/51323</Issue>
-        </ExcludeList>
         <ExcludeList Include="$(XunitTestBinBase)/JIT/opt/Devirtualization/Comparer_get_Default/*">
             <Issue>https://github.com/dotnet/runtime/issues/48190</Issue>
         </ExcludeList>
@@ -1239,9 +1221,6 @@
         <ExcludeList Include="$(XunitTestBinBase)/JIT/Directed/Convert/ldind_conv/**">
             <Issue>needs triage</Issue>
         </ExcludeList>
-        <ExcludeList Include="$(XunitTestBinBase)/JIT/Directed/Convert/signed_overflow_conversions_are_not_treated_as_unsigned/**">
-            <Issue>https://github.com/dotnet/runtime/issues/51323</Issue>
-        </ExcludeList>
         <ExcludeList Include="$(XunitTestBinBase)/JIT/Directed/coverage/compiler/FilterToHandler/**">
             <Issue>needs triage</Issue>
         </ExcludeList>