diff --git a/src/lib.rs b/src/lib.rs
index 8ca3e8d15e1..aff63c3c19d 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -27,6 +27,7 @@
     clippy::too_many_arguments,
     clippy::type_complexity,
     clippy::single_element_loop,
+    clippy::needless_return,
     // We are not implementing queries here so it's fine
     rustc::potential_query_instability
 )]
diff --git a/src/shims/backtrace.rs b/src/shims/backtrace.rs
index 9182b2a7217..bce4961339c 100644
--- a/src/shims/backtrace.rs
+++ b/src/shims/backtrace.rs
@@ -175,7 +175,7 @@ pub trait EvalContextExt<'mir, 'tcx: 'mir>: crate::MiriEvalContextExt<'mir, 'tcx
         // file would have more than 2^32 lines or columns, but whatever, just default to 0.
         let lineno: u32 = u32::try_from(lo.line).unwrap_or(0);
         // `lo.col` is 0-based - add 1 to make it 1-based for the caller.
-        let colno: u32 = u32::try_from(lo.col.0 + 1).unwrap_or(0);
+        let colno: u32 = u32::try_from(lo.col.0.saturating_add(1)).unwrap_or(0);
 
         let dest = this.force_allocation(dest)?;
         if let ty::Adt(adt, _) = dest.layout.ty.kind() {
diff --git a/src/shims/foreign_items.rs b/src/shims/foreign_items.rs
index e7cfd43f1b1..b9bd713d4d3 100644
--- a/src/shims/foreign_items.rs
+++ b/src/shims/foreign_items.rs
@@ -164,6 +164,9 @@ pub trait EvalContextExt<'mir, 'tcx: 'mir>: crate::MiriEvalContextExt<'mir, 'tcx
                     .expect("interpreting a non-executable crate");
                 for cnum in iter::once(LOCAL_CRATE).chain(
                     dependency_format.1.iter().enumerate().filter_map(|(num, &linkage)| {
+                        // We add 1 to the number because that's what rustc also does everywhere it
+                        // calls `CrateNum::new`...
+                        #[allow(clippy::integer_arithmetic)]
                         (linkage != Linkage::NotLinked).then_some(CrateNum::new(num + 1))
                     }),
                 ) {
@@ -542,7 +545,9 @@ pub trait EvalContextExt<'mir, 'tcx: 'mir>: crate::MiriEvalContextExt<'mir, 'tcx
                     .rev()
                     .position(|&c| c == val)
                 {
-                    let new_ptr = ptr.offset(Size::from_bytes(num - idx as u64 - 1), this)?;
+                    let idx = u64::try_from(idx).unwrap();
+                    #[allow(clippy::integer_arithmetic)] // idx < num, so this never wraps
+                    let new_ptr = ptr.offset(Size::from_bytes(num - idx - 1), this)?;
                     this.write_pointer(new_ptr, dest)?;
                 } else {
                     this.write_null(dest)?;
@@ -708,7 +713,9 @@ pub trait EvalContextExt<'mir, 'tcx: 'mir>: crate::MiriEvalContextExt<'mir, 'tcx
                 let a = this.read_scalar(a)?.to_u64()?;
                 let b = this.read_scalar(b)?.to_u64()?;
 
+                #[allow(clippy::integer_arithmetic)] // adding two u64 and a u8 cannot wrap in a u128
                 let wide_sum = u128::from(c_in) + u128::from(a) + u128::from(b);
+                #[allow(clippy::integer_arithmetic)] // it's a u128, we can shift by 64
                 let (c_out, sum) = ((wide_sum >> 64).truncate::<u8>(), wide_sum.truncate::<u64>());
 
                 let c_out_field = this.place_field(dest, 0)?;
diff --git a/src/shims/intrinsics/simd.rs b/src/shims/intrinsics/simd.rs
index 0c3241683a1..1b7ec591350 100644
--- a/src/shims/intrinsics/simd.rs
+++ b/src/shims/intrinsics/simd.rs
@@ -393,6 +393,8 @@ pub trait EvalContextExt<'mir, 'tcx: 'mir>: crate::MiriEvalContextExt<'mir, 'tcx
                 assert_eq!(bitmask_len, mask.layout.size.bits());
                 assert_eq!(dest_len, yes_len);
                 assert_eq!(dest_len, no_len);
+                let dest_len = u32::try_from(dest_len).unwrap();
+                let bitmask_len = u32::try_from(bitmask_len).unwrap();
 
                 let mask: u64 = this
                     .read_scalar(mask)?
@@ -401,18 +403,20 @@ pub trait EvalContextExt<'mir, 'tcx: 'mir>: crate::MiriEvalContextExt<'mir, 'tcx
                     .try_into()
                     .unwrap();
                 for i in 0..dest_len {
-                    let mask =
-                        mask & (1 << simd_bitmask_index(i, dest_len, this.data_layout().endian));
-                    let yes = this.read_immediate(&this.mplace_index(&yes, i)?.into())?;
-                    let no = this.read_immediate(&this.mplace_index(&no, i)?.into())?;
-                    let dest = this.mplace_index(&dest, i)?;
+                    let mask = mask
+                        & 1u64
+                            .checked_shl(simd_bitmask_index(i, dest_len, this.data_layout().endian))
+                            .unwrap();
+                    let yes = this.read_immediate(&this.mplace_index(&yes, i.into())?.into())?;
+                    let no = this.read_immediate(&this.mplace_index(&no, i.into())?.into())?;
+                    let dest = this.mplace_index(&dest, i.into())?;
 
                     let val = if mask != 0 { yes } else { no };
                     this.write_immediate(*val, &dest.into())?;
                 }
                 for i in dest_len..bitmask_len {
                     // If the mask is "padded", ensure that padding is all-zero.
-                    let mask = mask & (1 << i);
+                    let mask = mask & 1u64.checked_shl(i).unwrap();
                     if mask != 0 {
                         throw_ub_format!(
                             "a SIMD bitmask less than 8 bits long must be filled with 0s for the remaining bits"
@@ -485,9 +489,8 @@ pub trait EvalContextExt<'mir, 'tcx: 'mir>: crate::MiriEvalContextExt<'mir, 'tcx
                     let val = if src_index < left_len {
                         this.read_immediate(&this.mplace_index(&left, src_index)?.into())?
                     } else if src_index < left_len.checked_add(right_len).unwrap() {
-                        this.read_immediate(
-                            &this.mplace_index(&right, src_index - left_len)?.into(),
-                        )?
+                        let right_idx = src_index.checked_sub(left_len).unwrap();
+                        this.read_immediate(&this.mplace_index(&right, right_idx)?.into())?
                     } else {
                         span_bug!(
                             this.cur_span(),
@@ -551,12 +554,15 @@ pub trait EvalContextExt<'mir, 'tcx: 'mir>: crate::MiriEvalContextExt<'mir, 'tcx
                 assert!(dest.layout.ty.is_integral());
                 assert!(bitmask_len <= 64);
                 assert_eq!(bitmask_len, dest.layout.size.bits());
+                let op_len = u32::try_from(op_len).unwrap();
 
                 let mut res = 0u64;
                 for i in 0..op_len {
-                    let op = this.read_immediate(&this.mplace_index(&op, i)?.into())?;
+                    let op = this.read_immediate(&this.mplace_index(&op, i.into())?.into())?;
                     if simd_element_to_bool(op)? {
-                        res |= 1 << simd_bitmask_index(i, op_len, this.data_layout().endian);
+                        res |= 1u64
+                            .checked_shl(simd_bitmask_index(i, op_len, this.data_layout().endian))
+                            .unwrap();
                     }
                 }
                 this.write_int(res, dest)?;
@@ -583,10 +589,11 @@ fn simd_element_to_bool(elem: ImmTy<'_, Provenance>) -> InterpResult<'_, bool> {
     })
 }
 
-fn simd_bitmask_index(idx: u64, vec_len: u64, endianess: Endian) -> u64 {
+fn simd_bitmask_index(idx: u32, vec_len: u32, endianess: Endian) -> u32 {
     assert!(idx < vec_len);
     match endianess {
         Endian::Little => idx,
+        #[allow(clippy::integer_arithmetic)] // idx < vec_len
         Endian::Big => vec_len - 1 - idx, // reverse order of bits
     }
 }
diff --git a/src/shims/mod.rs b/src/shims/mod.rs
index f5b4de30a57..61829559245 100644
--- a/src/shims/mod.rs
+++ b/src/shims/mod.rs
@@ -1,3 +1,5 @@
+#![warn(clippy::integer_arithmetic)]
+
 mod backtrace;
 pub mod foreign_items;
 pub mod intrinsics;
diff --git a/src/shims/time.rs b/src/shims/time.rs
index 67303c47db7..d3c545ea58c 100644
--- a/src/shims/time.rs
+++ b/src/shims/time.rs
@@ -84,7 +84,7 @@ pub trait EvalContextExt<'mir, 'tcx: 'mir>: crate::MiriEvalContextExt<'mir, 'tcx
         Ok(0)
     }
 
-    #[allow(non_snake_case)]
+    #[allow(non_snake_case, clippy::integer_arithmetic)]
     fn GetSystemTimeAsFileTime(
         &mut self,
         LPFILETIME_op: &OpTy<'tcx, Provenance>,
diff --git a/src/shims/tls.rs b/src/shims/tls.rs
index a5205487981..ede4b12c2d2 100644
--- a/src/shims/tls.rs
+++ b/src/shims/tls.rs
@@ -63,6 +63,7 @@ impl<'tcx> Default for TlsData<'tcx> {
 impl<'tcx> TlsData<'tcx> {
     /// Generate a new TLS key with the given destructor.
     /// `max_size` determines the integer size the key has to fit in.
+    #[allow(clippy::integer_arithmetic)]
     pub fn create_tls_key(
         &mut self,
         dtor: Option<ty::Instance<'tcx>>,
diff --git a/src/shims/unix/fs.rs b/src/shims/unix/fs.rs
index 2a6499ce999..d3f4f5ef545 100644
--- a/src/shims/unix/fs.rs
+++ b/src/shims/unix/fs.rs
@@ -443,6 +443,7 @@ pub struct DirHandler {
 }
 
 impl DirHandler {
+    #[allow(clippy::integer_arithmetic)]
     fn insert_new(&mut self, read_dir: ReadDir) -> u64 {
         let id = self.next_id;
         self.next_id += 1;
diff --git a/src/shims/unix/linux/sync.rs b/src/shims/unix/linux/sync.rs
index b33553f4663..f9c97a23721 100644
--- a/src/shims/unix/linux/sync.rs
+++ b/src/shims/unix/linux/sync.rs
@@ -242,6 +242,7 @@ pub fn futex<'tcx>(
             // before doing the syscall.
             this.atomic_fence(AtomicFenceOrd::SeqCst)?;
             let mut n = 0;
+            #[allow(clippy::integer_arithmetic)]
             for _ in 0..val {
                 if let Some(thread) = this.futex_wake(addr_usize, bitset) {
                     this.unblock_thread(thread);
diff --git a/src/shims/windows/handle.rs b/src/shims/windows/handle.rs
index 443af1dfeaa..92e0a9a34e1 100644
--- a/src/shims/windows/handle.rs
+++ b/src/shims/windows/handle.rs
@@ -62,6 +62,7 @@ impl Handle {
         let floor_log2 = variant_count.ilog2();
 
         // we need to add one for non powers of two to compensate for the difference
+        #[allow(clippy::integer_arithmetic)] // cannot overflow
         if variant_count.is_power_of_two() { floor_log2 } else { floor_log2 + 1 }
     }
 
@@ -73,7 +74,7 @@ impl Handle {
     /// None of this layout is guaranteed to applications by Windows or Miri.
     fn to_packed(self) -> u32 {
         let disc_size = Self::packed_disc_size();
-        let data_size = u32::BITS - disc_size;
+        let data_size = u32::BITS.checked_sub(disc_size).unwrap();
 
         let discriminant = self.discriminant();
         let data = self.data();
@@ -86,7 +87,8 @@ impl Handle {
 
         // packs the data into the lower `data_size` bits
         // and packs the discriminant right above the data
-        discriminant << data_size | data
+        #[allow(clippy::integer_arithmetic)] // cannot overflow
+        return discriminant << data_size | data;
     }
 
     fn new(discriminant: u32, data: u32) -> Option<Self> {
@@ -101,12 +103,14 @@ impl Handle {
     /// see docs for `to_packed`
     fn from_packed(handle: u32) -> Option<Self> {
         let disc_size = Self::packed_disc_size();
-        let data_size = u32::BITS - disc_size;
+        let data_size = u32::BITS.checked_sub(disc_size).unwrap();
 
         // the lower `data_size` bits of this mask are 1
+        #[allow(clippy::integer_arithmetic)] // cannot overflow
         let data_mask = 2u32.pow(data_size) - 1;
 
         // the discriminant is stored right above the lower `data_size` bits
+        #[allow(clippy::integer_arithmetic)] // cannot overflow
         let discriminant = handle >> data_size;
 
         // the data is stored in the lower `data_size` bits