diff --git a/kernel/bpf/verifier.c b/kernel/bpf/verifier.c
index fb690539d5f6..022833903157 100644
--- a/kernel/bpf/verifier.c
+++ b/kernel/bpf/verifier.c
@@ -7258,6 +7258,7 @@ static int check_mem_size_reg(struct bpf_verifier_env *env,
 			      struct bpf_call_arg_meta *meta)
 {
 	int err;
+	const bool size_is_const = tnum_is_const(reg->var_off);
 
 	/* This is used to refine r0 return value bounds for helpers
 	 * that enforce this value as an upper bound on return values.
@@ -7272,7 +7273,7 @@ static int check_mem_size_reg(struct bpf_verifier_env *env,
 	/* The register is SCALAR_VALUE; the access check
 	 * happens using its boundaries.
 	 */
-	if (!tnum_is_const(reg->var_off))
+	if (!size_is_const)
 		/* For unprivileged variable accesses, disable raw
 		 * mode so that the program is required to
 		 * initialize all the memory that the helper could
@@ -7286,12 +7287,17 @@ static int check_mem_size_reg(struct bpf_verifier_env *env,
 		return -EACCES;
 	}
 
-	if (reg->umin_value == 0) {
-		err = check_helper_mem_access(env, regno - 1, 0,
-					      zero_size_allowed,
-					      meta);
-		if (err)
-			return err;
+	if (reg->umin_value == 0 && !zero_size_allowed) {
+		if (size_is_const) {
+			verbose(env, "R%d invalid zero-sized read\n", regno);
+		} else {
+			char tn_buf[48];
+
+			tnum_strn(tn_buf, sizeof(tn_buf), reg->var_off);
+			verbose(env, "R%d invalid possibly-zero-sized read: u64=[%#llx, %#llx] var_off=%s\n",
+				regno, reg->umin_value, reg->umax_value, tn_buf);
+		}
+		return -EACCES;
 	}
 
 	if (reg->umax_value >= BPF_MAX_VAR_SIZ) {
@@ -7299,9 +7305,21 @@ static int check_mem_size_reg(struct bpf_verifier_env *env,
 			regno);
 		return -EACCES;
 	}
+	/* If !zero_size_allowed, we already checked that umin_value > 0, so
+	 * umax_value should also be > 0.
+	 */
+	if (reg->umax_value == 0 && !zero_size_allowed) {
+		verbose(env, "verifier bug: !zero_size_allowed should have been handled already\n");
+		return -EFAULT;
+	}
 	err = check_helper_mem_access(env, regno - 1,
 				      reg->umax_value,
-				      zero_size_allowed, meta);
+				      /* zero_size_allowed: we asserted above that umax_value is
+				       * not zero if !zero_size_allowed, so we don't need any
+				       * further checks.
+				       */
+				      true ,
+				      meta);
 	if (!err)
 		err = mark_chain_precision(env, regno);
 	return err;
diff --git a/tools/testing/selftests/bpf/progs/verifier_helper_value_access.c b/tools/testing/selftests/bpf/progs/verifier_helper_value_access.c
index 692216c0ad3d..7c99c7bae09e 100644
--- a/tools/testing/selftests/bpf/progs/verifier_helper_value_access.c
+++ b/tools/testing/selftests/bpf/progs/verifier_helper_value_access.c
@@ -89,9 +89,14 @@ l0_%=:	exit;						\
 	: __clobber_all);
 }
 
+/* Call a function taking a pointer and a size which doesn't allow the size to
+ * be zero (i.e. bpf_trace_printk() declares the second argument to be
+ * ARG_CONST_SIZE, not ARG_CONST_SIZE_OR_ZERO). We attempt to pass zero for the
+ * size and expect to fail.
+ */
 SEC("tracepoint")
 __description("helper access to map: empty range")
-__failure __msg("invalid access to map value, value_size=48 off=0 size=0")
+__failure __msg("R2 invalid zero-sized read")
 __naked void access_to_map_empty_range(void)
 {
 	asm volatile ("					\
@@ -113,6 +118,38 @@ l0_%=:	exit;						\
 	: __clobber_all);
 }
 
+/* Like the test above, but this time the size register is not known to be zero;
+ * its lower-bound is zero though, which is still unacceptible.
+ */
+SEC("tracepoint")
+__description("helper access to map: possibly-empty range")
+__failure __msg("R2 invalid possibly-zero-sized read: u64=[0x0, 0x4] var_off=(0x0; 0x4)")
+__naked void access_to_map_possibly_empty_range(void)
+{
+	asm volatile ("                                         \
+	r2 = r10;                                               \
+	r2 += -8;                                               \
+	r1 = 0;                                                 \
+	*(u64*)(r2 + 0) = r1;                                   \
+	r1 = %[map_hash_48b] ll;                                \
+	call %[bpf_map_lookup_elem];                            \
+	if r0 == 0 goto l0_%=;                                  \
+	r1 = r0;                                                \
+	/* Read an unknown value */                             \
+	r7 = *(u64*)(r0 + 0);                                   \
+	/* Make it small and positive, to avoid other errors */ \
+	r7 &= 4;                                                \
+	r2 = 0;                                                 \
+	r2 += r7;                                               \
+	call %[bpf_trace_printk];                               \
+l0_%=:	exit;                                               \
+"	:
+	: __imm(bpf_map_lookup_elem),
+	  __imm(bpf_trace_printk),
+	  __imm_addr(map_hash_48b)
+	: __clobber_all);
+}
+
 SEC("tracepoint")
 __description("helper access to map: out-of-bound range")
 __failure __msg("invalid access to map value, value_size=48 off=0 size=56")
@@ -221,7 +258,7 @@ l0_%=:	exit;						\
 
 SEC("tracepoint")
 __description("helper access to adjusted map (via const imm): empty range")
-__failure __msg("invalid access to map value, value_size=48 off=4 size=0")
+__failure __msg("R2 invalid zero-sized read")
 __naked void via_const_imm_empty_range(void)
 {
 	asm volatile ("					\
@@ -386,7 +423,7 @@ l0_%=:	exit;						\
 
 SEC("tracepoint")
 __description("helper access to adjusted map (via const reg): empty range")
-__failure __msg("R1 min value is outside of the allowed memory range")
+__failure __msg("R2 invalid zero-sized read")
 __naked void via_const_reg_empty_range(void)
 {
 	asm volatile ("					\
@@ -556,7 +593,7 @@ l0_%=:	exit;						\
 
 SEC("tracepoint")
 __description("helper access to adjusted map (via variable): empty range")
-__failure __msg("R1 min value is outside of the allowed memory range")
+__failure __msg("R2 invalid zero-sized read")
 __naked void map_via_variable_empty_range(void)
 {
 	asm volatile ("					\
diff --git a/tools/testing/selftests/bpf/progs/verifier_raw_stack.c b/tools/testing/selftests/bpf/progs/verifier_raw_stack.c
index f67390224a9c..3dbda85e2997 100644
--- a/tools/testing/selftests/bpf/progs/verifier_raw_stack.c
+++ b/tools/testing/selftests/bpf/progs/verifier_raw_stack.c
@@ -64,7 +64,7 @@ __naked void load_bytes_negative_len_2(void)
 
 SEC("tc")
 __description("raw_stack: skb_load_bytes, zero len")
-__failure __msg("invalid zero-sized read")
+__failure __msg("R4 invalid zero-sized read")
 __naked void skb_load_bytes_zero_len(void)
 {
 	asm volatile ("					\
