diff --git a/lib/compat.c b/lib/compat.c
index 71738afe2..cc50ab1a7 100644
--- a/lib/compat.c
+++ b/lib/compat.c
@@ -184,23 +184,33 @@ char *do_big_num(int64 num, int human_flag, const char *fract)
 	if (human_flag > 1) {
 		unsigned int mult = human_flag == 2 ? 1000 : 1024;
 
-		if (abs_num >= mult) {
-			const char* units = " KMGTPE";
-			uint64_t powi = 1;
+		char units[] = "\0KMGTPE";
+		char *unit = units;
+		uint64_t powi = 1;
 
-			for (;;) {
-				if (abs_num / mult < powi)
-					break;
+		for (;;) {
+			if (abs_num / mult < powi)
+				break;
 
-				if (units[1] == '\0')
-					break;
+			if (unit[1] == '\0')
+				break;
+
+			powi *= mult;
+			++unit;
+		}
+		unit[1] = '\0';
+
+		if (powi > 1) {
+			unsigned int powj = 1, precision = 2;
 
-				powi *= mult;
-				++units;
+			for (; precision > 0; precision--) {
+				powj *= 10;
+				if (abs_num / powi < powj)
+					break;
 			}
 
-			snprintf(bufs[n], sizeof bufs[0], "%.2f%c",
-				(double) num / powi, *units);
+			snprintf(bufs[n], sizeof bufs[0], "%.*f%s%s", precision,
+				(double) num / powi, unit, *unit && mult == 1024 ? "i" : "");
 			return bufs[n];
 		}
 	}
diff --git a/progress.c b/progress.c
index 7a241a962..cb1af376a 100644
--- a/progress.c
+++ b/progress.c
@@ -69,7 +69,6 @@ static unsigned long msdiff(struct timeval *t1, struct timeval *t2)
 static void rprint_progress(OFF_T ofs, OFF_T size, struct timeval *now, int is_last)
 {
 	char rembuf[64], eol[128];
-	const char *units;
 	unsigned long diff;
 	double rate, remain;
 	int pct;
@@ -93,7 +92,7 @@ static void rprint_progress(OFF_T ofs, OFF_T size, struct timeval *now, int is_l
 		/* Compute stats based on the starting info. */
 		if (!ph_start.time.tv_sec || !(diff = msdiff(&ph_start.time, now)))
 			diff = 1;
-		rate = (double) (ofs - ph_start.ofs) * 1000.0 / diff / 1024.0;
+		rate = (double) (ofs - ph_start.ofs) * 1000.0 / diff;
 		/* Switch to total time taken for our last update. */
 		remain = (double) diff / 1000.0;
 	} else {
@@ -101,18 +100,8 @@ static void rprint_progress(OFF_T ofs, OFF_T size, struct timeval *now, int is_l
 		/* Compute stats based on recent progress. */
 		if (!(diff = msdiff(&ph_list[oldest_hpos].time, now)))
 			diff = 1;
-		rate = (double) (ofs - ph_list[oldest_hpos].ofs) * 1000.0 / diff / 1024.0;
-		remain = rate ? (double) (size - ofs) / rate / 1000.0 : 0.0;
-	}
-
-	if (rate > 1024*1024) {
-		rate /= 1024.0 * 1024.0;
-		units = "GB/s";
-	} else if (rate > 1024) {
-		rate /= 1024.0;
-		units = "MB/s";
-	} else {
-		units = "kB/s";
+		rate = (double) (ofs - ph_list[oldest_hpos].ofs) * 1000.0 / diff;
+		remain = rate ? (double) (size - ofs) / rate : 0.0;
 	}
 
 	if (remain < 0 || remain > 9999.0 * 3600.0)
@@ -127,8 +116,8 @@ static void rprint_progress(OFF_T ofs, OFF_T size, struct timeval *now, int is_l
 	output_needs_newline = 0;
 	pct = ofs == size ? 100 : (int) (100.0 * ofs / size);
 	rput_progress();
-	rprintf(FCLIENT, "%15s %3d%% %7.2f%s %s%s",
-		human_num(ofs), pct, rate, units, rembuf, eol);
+	rprintf(FCLIENT, "%15sB %3d%% %7sB/s %s%s", human_num(ofs), pct,
+		rate >= INT64_MAX ? ">MAX " : human_num((int64)rate), rembuf, eol);
 	if (!is_last && !quiet) {
 		output_needs_newline = 1;
 		rflush(FCLIENT);
diff --git a/rsync.1.md b/rsync.1.md
index bab9257ce..4fb2ff149 100644
--- a/rsync.1.md
+++ b/rsync.1.md
@@ -3616,7 +3616,11 @@ sign) if you want the local shell to expand it.
     The unit letters that are appended in levels 2 and 3 are: `K` (kilo), `M`
     (mega), `G` (giga), `T` (tera), `P` (peta) or `E` (exa). For example, a
     1234567-byte file would output as 1.23M in level-2 (assuming that a
-    period is your local decimal point).
+    period is your local decimal point). Dynamic precision is applied, so the
+    three most-significant digits are shown (for example: 3.45M -> 46.7M ->
+    523M -> 1.24G -> ...).
+    Additionally an `i` is appended in level-3 to indicate the binary base.
+    The same file would output as 1.17Mi in level-3.
 
     Backward compatibility note: versions of rsync prior to 3.1.0 (September 2013) do not
     support human-readable level 1, and they default to level 0.  Thus,
@@ -3784,10 +3788,10 @@ sign) if you want the local shell to expand it.
     While rsync is transferring a regular file, it updates a progress line that
     looks like this:
 
-    >     782448  63%  110.64kB/s    0:00:04
+    >     782,448B  63% 113,295B/s    0:00:04
 
-    In this example, the receiver has reconstructed 782448 bytes or 63% of the
-    sender's file, which is being reconstructed at a rate of 110.64 kilobytes
+    In this example, the receiver has reconstructed 782,448 bytes or 63% of the
+    sender's file, which is being reconstructed at a rate of 113,295 bytes
     per second, and the transfer will finish in 4 seconds if the current rate
     is maintained until the end.
 
@@ -3801,11 +3805,11 @@ sign) if you want the local shell to expand it.
     When the file transfer finishes, rsync replaces the progress line with a
     summary line that looks like this:
 
-    >     1,238,099 100%  146.38kB/s    0:00:08  (xfr#5, to-chk=169/396)
+    >     1,238,099B 100% 149,893B/s    0:00:08  (xfr#5, to-chk=169/396)
 
     In this example, the file was 1,238,099 bytes long in total, the average
-    rate of transfer for the whole file was 146.38 kilobytes per second over
-    the 8 seconds that it took to complete, it was the 5th transfer of a
+    rate of transfer for the whole file was 149,893 bytes per second over the
+    8 seconds that it took to complete, it was the 5th transfer of a
     regular file during the current rsync session, and there are 169 more files
     for the receiver to check (to see if they are up-to-date or not) remaining
     out of the 396 total files in the file-list.
diff --git a/testsuite/output-options_test.py b/testsuite/output-options_test.py
index 325d828a1..be68297be 100644
--- a/testsuite/output-options_test.py
+++ b/testsuite/output-options_test.py
@@ -95,8 +95,9 @@ def out(*args, want_rc=0, env=None, text=True):
 # --- --progress shows a percentage ------------------------------------------
 rmtree(TODIR)
 p = out('-a', '--progress', f'{src}/', f'{TODIR}/')
-if '100%' not in p.stdout:
-    test_fail(f"--progress did not show a percentage:\n{p.stdout}")
+progress_re = r'[\d.,]+B\s+100%\s+[\d.,]+B/s\s+\d+:\d\d:\d\d'
+if not re.search(progress_re, p.stdout):
+    test_fail(f"--progress did not show the expected final shape:\n{p.stdout}")
 
 # --quiet must suppress the progress carriage return as well as its text.
 rmtree(TODIR)
@@ -121,6 +122,28 @@ def out(*args, want_rc=0, env=None, text=True):
 if re.search(suffix_re, plain):
     test_fail(f"--stats without -h unexpectedly used a unit suffix:\n{plain}")
 
+rmtree(TODIR)
+human_binary = out('-a', '-hh', '--stats', f'{src}/', f'{TODIR}/').stdout
+if 'Total file size: 48.8Ki bytes' not in human_binary:
+    test_fail(f"-hh did not use dynamic binary-unit precision:\n{human_binary}")
+
+rmtree(src)
+rmtree(TODIR)
+makepath(src)
+make_data_file(src / 'threshold', 1024)
+threshold = out('-a', '-hh', '--stats', f'{src}/', f'{TODIR}/').stdout
+if 'Total file size: 1.00Ki bytes' not in threshold:
+    test_fail(f"-hh did not show an exact-threshold binary unit:\n{threshold}")
+
+rmtree(src)
+rmtree(TODIR)
+makepath(src)
+make_data_file(src / 'below-threshold', 1000)
+below_threshold = out('-a', '-hh', '--stats', f'{src}/', f'{TODIR}/').stdout
+if 'Total file size: 1,000 bytes' not in below_threshold:
+    test_fail("-hh should preserve raw byte formatting below the binary-unit "
+              f"threshold:\n{below_threshold}")
+
 # --- -8 / --8-bit-output leaves high-bit filename bytes unescaped ------------
 # rsync escapes non-printable name bytes as \#NNN; -8 prints 8-bit bytes raw.
 # This needs a filename containing a high-bit byte and a C locale (where such a