diff --git a/src/xz/coder.c b/src/xz/coder.c
index 4786e375..e6ed3e55 100644
--- a/src/xz/coder.c
+++ b/src/xz/coder.c
@@ -244,15 +244,13 @@ coder_set_compression_settings(void)
 		if (!preset_default)
 			message(V_WARNING, _("Adjusted LZMA%c dictionary size "
 					"from %s MiB to %s MiB to not exceed "
-					"the memory usage limit of %s"),
+					"the memory usage limit of %s MiB"),
 					filters[i].id == LZMA_FILTER_LZMA2
 						? '2' : '1',
 					uint64_to_str(orig_dict_size >> 20, 0),
 					uint64_to_str(opt->dict_size >> 20, 1),
-					uint64_to_nicestr(memory_limit,
-							NICESTR_B,
-							NICESTR_MIB,
-							false, 2));
+					uint64_to_str(round_up_to_mib(
+						memory_limit), 2));
 	}
 
 /*
diff --git a/src/xz/message.c b/src/xz/message.c
index ef583fa8..b5244d44 100644
--- a/src/xz/message.c
+++ b/src/xz/message.c
@@ -852,14 +852,35 @@ message_mem_needed(enum message_verbosity v, uint64_t memusage)
 	if (v > verbosity)
 		return;
 
-	// NOTE: With bad luck, the rounded values may be the same, which
-	// can be confusing to the user when this function is called to
-	// tell that the memory usage limit was too low.
-	message(v, _("%s of memory is required. The limit is %s."),
-			uint64_to_nicestr(memusage,
-				NICESTR_B, NICESTR_MIB, false, 0),
-			uint64_to_nicestr(hardware_memlimit_get(),
-				NICESTR_B, NICESTR_MIB, false, 1));
+	// Convert memusage to MiB, rounding up to the next full MiB.
+	// This way the user can always use the displayed usage as
+	// the new memory usage limit. (If we rounded to the nearest,
+	// the user might need to +1 MiB to get high enough limit.)
+	memusage = round_up_to_mib(memusage);
+
+	// 2^64 with thousand separators + " MiB" suffix + '\0' = 26 + 4 + 1
+	char memlimitstr[32];
+
+	// Show the memory usage limit as MiB unless it is less than 1 MiB.
+	// This way it's easy to notice errors where one has typed
+	// --memory=123 instead of --memory=123MiB.
+	uint64_t memlimit = hardware_memlimit_get();
+	if (memlimit < (UINT32_C(1) << 20)) {
+		snprintf(memlimitstr, sizeof(memlimitstr), "%s B",
+				uint64_to_str(memlimit, 1));
+	} else {
+		// Round up just like with memusage. If this function is
+		// called for informational purporse (to just show the
+		// current usage and limit), we will never show that
+		// the usage is higher than the limit, which would give
+		// a false impression that the memory usage limit isn't
+		// properly enforced.
+		snprintf(memlimitstr, sizeof(memlimitstr), "%s MiB",
+				uint64_to_str(round_up_to_mib(memlimit), 1));
+	}
+
+	message(v, _("%s MiB of memory is required. The limit is %s."),
+			uint64_to_str(memusage, 0), memlimitstr);
 
 	return;
 }
diff --git a/src/xz/util.c b/src/xz/util.c
index 784f6d30..dd95fa7a 100644
--- a/src/xz/util.c
+++ b/src/xz/util.c
@@ -119,6 +119,13 @@ error:
 }
 
 
+extern uint64_t
+round_up_to_mib(uint64_t n)
+{
+	return (n >> 20) + ((n & ((UINT32_C(1) << 20) - 1)) != 0);
+}
+
+
 extern const char *
 uint64_to_str(uint64_t value, uint32_t slot)
 {
diff --git a/src/xz/util.h b/src/xz/util.h
index 67bf3075..2e08b4a8 100644
--- a/src/xz/util.h
+++ b/src/xz/util.h
@@ -41,6 +41,12 @@ extern uint64_t str_to_uint64(const char *name, const char *value,
 		uint64_t min, uint64_t max);
 
 
+/// \brief      Round an integer up to the next full MiB and convert to MiB
+///
+/// This is used when printing memory usage and limit.
+extern uint64_t round_up_to_mib(uint64_t n);
+
+
 /// \brief      Convert uint64_t to a string
 ///
 /// Convert the given value to a string with locale-specific thousand